Spline functions: Basic theory, third edition

Spline Functions: Basic Theory, Third Edition

Volumn , Issue , 2007, Pages 1-582

  Schumaker, Larry ^a  

^a VANDERBILT UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85010383584     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511618994     Document Type: Book

References (691)

1. Achieser, N. I. [1956] Theory of Approximation, Ungar, New York.
2. Adams, R. A. [1975] Sobolev Spaces, Academic Press, New York.
3. Ahlberg, J. H. [1969] "Splines in the complex plane," in Schoenberg [1969b], pp. 1-27.
4. Ahlberg, J. H. and E. N. Nilson [1963] "Convergence properties of the spline fit," SIAM J. 11, 95-104.
5. Ahlberg, J. H. and E. N. Nilson [1966] "The approximation of linear functionals," SIAM J. Numer. Anal., 3, 173-182.
6. Ahlberg, J. H., E. N. Nilson, and J. L. Walsh [1964] "Fundamental properties of generalized splines," Proc. Nat. Acad Sci. U.S.A., 52, 1412-1419.
7. Ahlberg, J. H., E. N. Nilson, and J. L. Walsh [1965d] "Best approximation and convergence properties of higher-order spline approximations," J. Math. Mech., 14, 231-244.
8. Ahlberg, J. H., E. N. Nilson, and J. L. Walsh [l965b] "Extremal, orthogonality, and convergence properties of multidimensional splines," J. Math. Anal. Appl., 12, 27-48.
9. Ahlberg, J. H., E. N. Nilson, and J. L. Walsh [1965c] "Convergence properties of generalized splines," Proc. Nat. Acad Sci. U.S.A., 54, 344-350.
10. Ahlberg, J. H., E. N. Nilson, and J. L. Walsh [1967a] "Complex cubic splines," Trans. Am. Math. Soc., 129, 391-413.
11. Ahlberg, J. H., E. N. Nilson, and J. L. Walsh [1967b] The Theory of Splines and Their Applications, Academic Press, New York.
12. Ahlberg, J. H., E. N. Nilson, and J. L. Walsh [1969] "Properties of analytic splines (1). Complex polynomial splines," J. Math. Anal. Appl., 27, 262-278.
13. Ahlberg, J. H., E. N. Nilson, and J. L. Walsh [1971] "Complex polynomial splines on the unit circle," J. Math. Anal. Appl., 33, 234-257.
14. Arthur, D. W. [1974] "Multivariate spline functions. I. Construction, properties, and computation," J. Approximation Theory, 12, 396-411.
15. Arthur, D. W. [1975] "Multivariate spline functions. II. Best error bounds," J. Approximation Theory, 15, 1-10.
16. Asker, B. [1962] "The spline curve, a smooth interpolating function used in numerical design of ship lines," BIT, 2, 76-82.
17. Astor, P. H., and C. S. Duris [1974] "Discrete L-splines," Numer. Math., 22, 393-402.
18. Atkinson, K. [1968] "On the order of convergence of natural cubic spline interpolation problems," SIAM J. Numer. Anal., S, 89-101.
19. Atteia, M. [1965a] "Spline-fonctions généralisées," C. R. Acad. Sci. Paris Sere A, 261, 2149-2152.
20. Atteia, M. [1965b] "Généralisation de la definition et des proprietes des spline-fonctions" C. R. Acad. Sci. Paris Sere A, 260, 3550-3553.
21. Atteia, M. [1966a] "Étude de certains noyaux et theorie des fonctions spline en Analysis Numerique," dissertation, Grenoble.
22. Atteia, M. [1966b] "Existence et determination des fonctions splines aplusieurs variables," C. R. Acad. Sci. Paris Sere A, 262, 575-578.
23. Aubin, J.-Po [1967] "Behavior of the error of the approximate solution of boundary value problems for linear elliptic operators by Galerkins and finite difference methods," Ann. Scuola Norm. Pisa, 21, 599-637.
24. Atteia, M. [1972] Approximation of Elliptic Boundary-Value Problems, Wiley, New York.
25. Aumann, G. [1963] "Approximation by step functions," Proc. Am. Math. Soc., 14, 477-482.
26. p space, p;> I," (Russian), A. N. Usb. SSR. Sere Fiz.-Mat., 2, 24-30.
27. Babuska, I. [1970] "Approximation by hill functions," Comment. Math. Univ. Carolinae, 11, 787-811.
28. p[0,1] and C[O, I]," Am. J. Math., 154, 437-457.
29. Bartelt, M. W. [1975] "Weak Chebychev sets and splines," J. Approximation Theory, 14, 30-37.
30. Bastien, R. and J. Dubuc [1976] "Systemes Faibles de Tchebycheff et Polynomes de Bernstein," Canad J. Math., 28, 653-658.
31. Baum, A. M. [1976a] "An algebraic approach to simply hyperbolic splines on the real line," J. Approximation Theory, 17, 189-199.
32. Baum, A. M. [1976b] "Double hyperbolic splines on the real line," J. Approximation Theory, 18, 174-188.
33. Beckenbach, E. F., and R. Bellman [1961] IneflUtJlities, Cambridge University Press.
34. Bellman, R., and R. Roth [1969] "Curve fitting by segmented straight lines," J. Am. Statist. Assoc., 64, 1079-1084.
35. Berger, S. A., and W. C. Webster [1963] "An application of linear programming to the fairing of ships lines," in Recent Advances in Mathematical Programming, R. L. Graves and P. Wolfe, Eds., McGraw-Hill, New York, pp. 241-253.
36. Berger, S. A., W. C. Webster, R. A. Tapia, and D. A. Atkins [1966] "Mathematical ship lofting," J. Ship Research, 10, 203-222.
37. p," Bollettino U.M.I., 10, 632-648.
38. Bernstein, S. N. [1926] Lecons sur les Propriétés Extremales et la Meillure Approximation des Fonctions Analytiques d’une Variable Realle, Gauthier-Villars, Paris.
39. Birkhoff, G. D. [1906] "General mean value and remainder theorems with applications to mechanical differentiation and quadrature," Trans. Am. Math. Soc., 7, 107-136.
40. Birkhoff, G. [1967] "Local spline approximation by moments," J. Math. Mech., 16, 987-990.
41. Birkhoff, G. [1969] "Piecewise bicubic interpolation and approximation in polygons," in Schoenberg [1969b], pp. 185-221.
42. Birkhoff, G., and C. deBoor [1964] "Error bounds for spline interpolation," J. Matk Meek 13, 827-836.
43. Birkhoff, G., and C. deBoor [1965] "Piecewise polynomial interpolation and approximation" in Garabedian [1965], pp. 164-190.
44. Birkhoff, G. and H. Garabedian [1960] "Smooth surface interpolation," J. Math. and Phys., 39, 258-268.
45. Birkhoff, G., M. H. Schultz, and R. S. Varga [1968] "Piecewise Hermite interpolation in one and two variables with applications to partial differential equations," Numer. Math., 11, 232-256.'
46. Birman, M. S. and M. Z. Solomjak [1966] "Approximation of the functions of the classes Wαp by piecewise polynomial functions" (Russian), Soviet Math. Dokl., 7, 1573-1577; see also Dokl. Akad Nauk SSSR, 171, 1015-1018.
47. Birman, M. S. and M. Z. Solomjak [1967] "Piecewise polynomial approximations of functions of the classesWα p" (Russian), Math. USSR Sh., 2, 295-371; see also Mat. Sb., 73, 331-355.
48. Bohmer, K. [1974] Spline-Funktionen, Teubner-Studienbucher, Stuttgart.
49. Bohmer, K., G. Meinardus, and W. Schempp [1974] Spline Funktionen, Eds., Bibliographisches Institut, Zurich.
50. Bohmer, K., G. Meinardus, and W. Schempp [1976] Spline Functions, Karlsruhe 1975, Eds., Springer-Verlag Lecture Notes 501, Heidelberg.
51. deBoor, C. [1962] "Bicubic spline interpolation," J. Math. Phys., 41, 212-218.
52. deBoor, C.[1963] "Best approximation properties of spline functions of odd degree," J. Math. Mech., 12, 747-749.
53. deBoor, C.[1966] "The method of projections, etc.," PhD. Dissertation, University of Michigan.
54. deBoor, C.[1968a] "On the convergence of odd-degree spline interpolation," J. Approximation Theory, 1, 452-463.
55. deBoor, C.[1968b] "On local spline approximation by moments," J. Math. Meek, 17, 729-736.
56. deBoor, C.[1968c] "On uniform approximation by splines," J. Approximation Theory, 1, 219-235.
57. deBoor, C.[1972] "On calculating with B-splines," J. Approximation Theory, 6, 50-62.
58. deBoor, C.[1973a] "The quasi-interpolant as a tool in elementary polynomial spline theory," in Lorentz (1973), pp. 269-276.
59. deBoor, C.[1973b] "Good approximation by splines with variable knots," in Meir and Sharma [1973], pp. 57-72.
60. deBoor, C.[1974a] "A smooth and local interpolation with "small" kth derivative," in Numerical Solutions for Ordinary Differential Equations, A. Ariz, ed., Academic Press, New York, pp. 177-197.
61. deBoor, C.[1974b] "A remark concerning perfect splines," Bull. Am. Math. Soc., 80, 723-727.
62. deBoor, C.[1975] "How small can one make the derivatives of an interpolating function," J. Approximation Theory, 13, 105-116.
63. deBoor, C.[1976a] "Total positivity of the spline collocation matrix," IndiaM Univ. J. Math., 15, 541-551.
64. deBoor, C.[1976b] "Splines as linear combinations of B-splines. A survey," in Lorentz, Chui, and Schumaker [1976], pp. 1-47.
65. deBoor, C.[1976c] "On local linear functionals which vanish at all B-splines but one," in Law and Sahney [1976], pp. 120-145.
66. deBoor, C.deBoor, C.[1977] "Subroutine package for calculating with B-splines," SIAM J. Numer. AMl., 14, 441-472.
67. deBoor, C.[1978] A Practical Guide to Splines, Springer-Verlag, New York.
68. deBoor, C. and G. J. Fix [1973] "Spline approximation by quasi-interpolants," J. Approximation TMory,8, 19-45.
69. deBoor, C., T. Lyche, and L. L. Schumaker [1976] "On calculating with B-splines II. Integration." in Numerische Methoden tier Approximations Theorie, Band 3, ISNM Vol. 30, Birkhauser, pp. 123-146.
70. deBoor, C., and R. E. Lynch [1966] "On splines and their minimum properties," J. Math. Meeh., 15,953-969.
71. deBoor, C., and A. Pinkus [1977] "Backward error analysis for totally positive linear systems," N-r. Math., 17, 485-490.
72. deBoor, C., and I. J. Schoenberg [1976] "Cardinal interpolation and spline functions VIII. The Budan-Fourier theorem for splines and applications," in Bohmer, Meinardus, and Schempp [1976], pp. 1-79.
73. Braess, D. [1971] "Chebyshev approximation by spline functions with free knots," Numer. Matk, 17, 357-366.
74. Braess, D. [1974] "Rationale Interpolation, Normalitat und Monosplines," Numer. Math., 22, 219-232.
75. Braess, D. [1975] "On the degree of approximation by spline functions with free knots," Aequationes Math., 12, 80-81.
76. Bramble, J. H., and S. R. Hilbert [1970] "Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation," SIAM J. Numer. Anal., 7, 112-124.
77. Braess, D. [1971] "Bounds for a class of linear functionals with applications to Hermite interpolation," Numer. Math., 16, 362-369.
78. Brudnyi, Ju. A. [1964] "On a theory of local best approximation" (Russian), Kazan. Gos. Usen. Zap., 124, 43-49.
79. Brudnyi, Ju. A. [1970] "A multidimensional analog of a theorem of Whitney," (Russian) Math. USSR. Sh., 11, 157-170.
80. Brudnyi, Ju. A. [1971] "Piecewise polynomial approximation and local approximations," Soviet Math. Dokl., 12, 1591-1594.
81. Brudnyi, Ju. A. [1974a] "Local approximation and differential properties of functions of several variables" (Russian), Uspehi Mat. Nauk, 29, 163-164.
82. Brudnyi, Ju. A. [1974b] "Spline approximation and functions of bounded variation," Soviet Math. Dokl., 15,518-521.
83. Brudnyi, Ju. A. [1976] "Piecewise polynomial approximation, embedding theorem and rational approximation," in Schaback and Scherer [1976], pp. 73-98.
84. Brudnyi, Ju. A., and I. E. Gopengauz [1963] "Approximation by piecewise polynomial functions" (Russian), Izv. Akad Nauk SSSR Ser. Mat., 27, 723-746.
85. Burchard, H. G. [1968] "Interpolation and approximation by generalized convex functions," Dissertation, Purdue.
86. Burchard, H. G.[1973] "Extremal positive splines with applications," in Lorentz [1973], pp. 291-294.
87. Burchard, H. G.[1974] "Splines (with optimal knots) are better," J. Applicable Analysis, 3, 309-319.
88. Burchard, H. G.[1977] "On the degree of convergence of piecewise polynomial approximation on optimal meshes II," Trans. Am. Math. Soc., 234, 531-559.
89. Burchard, H. G., and D. F. Hale [1975] "Piecewise polynomial approximation on optimal meshes," J. Approximation Theory, 14, 128-147.
90. Burenkov, V. I. [1974] "Sobolev’s integral representation and Taylor’s Formula," Trudy Mat. Inst. Steklow, 131, 33-38.
91. Burkbill, H. [1961] "On Riesz and Riemann summability," Proc. Cambridge Philos. Soc., 57, 55-60.
92. psaturation theorem for splinesl’ Canad. J. Math., 24, 957-966.
93. Butterfield, K. R. [1976] "The computation of all the derivatives of a B-spline basis," J. Inst. Math. Appl., 17, 15-25.
94. Butzer, P. L., and H. Berens [1967] Semi-groups of Operators and Approximation, Springer-Verlag, Berlin.
95. Butzer, P. L., and K. Scherer [1969] "On the fundamental approximation theorems of D. Jackson, S. N. Bernstein, and theorems of M. Zamansky and S. B. Steckin," Aequotiones Math., 3, 170-185.
96. Butzer, P. L., and K. Scherer [1970] "On fundamental theorems of approximation theory and their dual versions," J. Approximation Theory, 3, 87-100.
97. Cavaretta, A. S. [1975] "Oscillatory and zero properties for perfect splines and monosplines," J. Analyse Math., 28, 41-59.
98. Cheney, E. W. [1966] Introduction to Approximation Theory, McGraw Hill, New York.
99. Cheney, E. W., and F. Schurer [1968] "A note on the operators arising in spline approximation," J. Approximation Theory, 1, 94-102.
100. Cheney, E. W., and F. Schurer [1970] "Convergence of cubic spline interpolants;l’ J. Approximation Theory, 3, 114-116.
101. Chernik, N. E. [1975] "Approximation by splines with fixed knots," (Russian) Proc. Steklov. Inst. Math., 138, 174-199.
102. Ciesielski, Z. [1975] "Spline bases in function spaces," in Ciesielski and Musielak [1975], pp. 49-54.
103. Ciesielski, Z., and J. Musielak [1975] Approximation Theory, Eds., Reidel Publishing Co., Holland (also PWN-Polish Scientific Publishers, Warsaw).
104. Conte, S., and C. deBoor [1972] Elementary Numerical Analysis, 2nd edition, McGraw Hill, New York.
105. Cox, M. G. [1971] "Curve fitting with piecewise polynomials," J. Inst. Math. Appl., 8, 36-52.
106. Cox, M. G. [1972] "The numerical evaluation of B-splines," J. Inst. Math. App., 10, 134-149.
107. Curry, H. B. [1947] Review, Math. Tables & Other Aids to Computation, 2, 167-169,211-213.
108. Curry, H. B., and I. J. Schoenberg [1947] "On spline distributions and their limits: the Polya distribution functions," Abstract 380t, Bull. Am. Math. Soc., 53, 1114.
109. Curry, H. B., and I. J. Schoenberg [1966] "On Pólya frequency functions IV: The fundamental spline functions and their limits," J. Analyse Math., 17, 71-107.
110. Dahmen, G., R. DeVore, and K. Scherer (1980) "Multidimensional spline approximation," SIAM J. Numer. Anal., 15 (1980), 380-402.
111. Davis, P. J. [1963] Interpolation and Approximation, Blaisdell, New York.
112. delaVallee Poussin, C. J. [1919] Lecons sur I’Approximation des Fonctions d’une Variable Real/e, Gauthier-Villars, Paris.
113. Demko, S. [1977] "Local approximation properties of spline projections," J. Approximation Theory, 19, 176-185.
114. Demko, S., and R. S. Varga [1974] "Extended 4 error bounds for spline and L-spline interpolation," J. Approximation Theory, 12, 242-264.
115. DeVore, R. [1968] "On Jackson’s Theorem," J. Approximation Theory, 1, 314-318.
116. DeVore, R. [1972] Approximation of Continuous Functions by Positive Linear Operators, Springer Lecture Notes in Mathematics, No. 293, Springer, Berlin.
117. DeVore, R. [1976] "Degree of approximation," in Lorentz, Chui, and Schumaker (1976), pp. 117-16l.
118. DeVore, R. [1977a] "Monotone approximation by polynomials," SIAM J. Math. Anal., 8, 906-921.
119. DeVore, R. [1977b] "Monotone approximation by splines," SIAM J. Math. Anal., 8, 891-905.
120. DeVore, R. [1977c] "Pointwise approximation by polynomials and splines," in Constructive Function Theory, Akad. Nauk SSSR, Moscow, pp. 132-141.
121. DeVore, R. A., and F. Richards [1973a] "The degree of approximation by Chebyshevian splines," Trans. Am. Math. Soc., 181,401-418.
122. DeVore, R. A., and F. Richards [1973b] "Saturation and inverse theorems for spline approximation" in Meir and Sharma [1973], pp. 73-82.
123. DeVore, R. A., and K. Scherer [1976] "A constructive theory for approximation by splines with an arbitrary sequence of knot sets" in Schaback and Scherer [1976], pp. 167-183.
124. Di Guglielmo, F. [1969] "Construction d’approximation des espaces de Sobolev sur des reseaux en simplexes," Calcolo, 6, 279-331.
125. Dodson, D. S. [1972] "Optimal order approximation by polynomial spline functions," Ph.D. thesis, Purdue University, West Lafayette.
126. Domsta, J. [1972] "A theorem on B-splines," Studia Math., 41, 291-314.
127. Domsta, J. [1976] "A theorem on B-splines II. The periodic case," Bull. Acad Polon. Sci. Ser. Sci. Math. Astron. Phys., 24, 1077-1084.
128. Dupont, T., and R. Scott [1978] "Constructive polynomial approximation," in Recent Advances in Numerical Analysis, C. deBoor and G. Golub, Eds., Academic Press, New York.
129. Dupont, T., and R. Scott [1980] "Polynomial approximation of functions in Sobolov spaces," Math. of Compo 34, 441-463.
130. Dunford, N., and J. T. Schwartz [1957] Linear Operators, Part I, Wiley Interscience, New York.
131. Eagle, A. [1928] "On the relation between the Fourier constants of a periodic function and the coefficients determined by harmonic analysis," Phil. Mag., 5, 113-132.
132. Edwards, R. E. [1965] Functional Analysis, Theory and Applications, Holt, Rinehart and Winston, New York.
133. El Kolli, A. [1974] "Niéme épaisseur dans les espaces de Sobolev," J. Approximation Theory, 10, 268-294.
134. Faber, G. [1914] "Uber die interpolatorische Darstellung Stetiger Funktionen" Deutsch. Math. Verein, 23, 192-210.
135. Favard, J. [1940] "Sur l’interpolation," J. Math. Pures Appl. (9), 19,281-306.
136. Ferguson, D. [1973] "Sufficient conditions for the Peano kernel to be one sign," SIAM J. Numer. Anal., 10, 1047-1054.
137. Ferguson, D. [1974] "Sign changes and minimal support properties of Hermite-Birkhoff splines with compact support," SIAMJ. Numer. Anal., 11, 769-779.
138. Fisher, S. D., and J. W. Jerome [1975] "Minimum Extremals in Function Spaces," Springer Verlag Lecture Notes 479, Heidelberg.
139. Fitzgerald, C. H., and L. L. Schumaker [1969] "A differential equation approach to interpolation at extremal points," J. Analyse Math., 22, 117-134.
140. Fix, G., and G. Strang [1969] "Fourier analysis of the finite element method in Ritz-Galerkin theory," Studies Appl. Math., 48, 265-273.
141. Fowler, A. H., and C. W. Wilson [1963] "Cubic spline, a curve fitting routine," Report Y-I400, Oak Ridge.
142. Freud, G. [1970] "Some questions that are related to approximation by spline functions and polynomials" (Russian), Studia Sci. Math. Hungar., 5, 161-171.
143. Freud, G., and V. Popov [1969] "On approximation by spline functions," Proc. Conf. on Constructive Theory of Functions, G. Alexits and S. B. Stechkin, Eds., Akademia Kiado, Budapest, pp. 163-172.
144. Friedman, A. [1969] Partial Differential Equations, Holt, Rinehart and Winston, New York.
145. Gaffney, P. W. [1974] "The calculation of indefinite integrals of B-splines," CSS 16, AERE Harwell.
146. Gaier, D. [1970] "Saturation bei Spline-Approximation und Quadratur," Numer. Math., 16, 129-140.
147. Garabedian, H. L. [1965] Approximation of Functions, Elsevier, Amsterdam.
148. Glaeser, G. [1967] "Prolongement extremal de fonctions differentiables," Publ. Sect. Math. Faculte des Sciences Rennes, France.
149. Glaeser, G. [1973] "Prolongement extremal de fonctions differentiables d’une variable," J. Approximation Theory, 8, 249-261.
150. Gluskin, E. [1974] "On a problem concerning diameters," Soo. Math. Dokl. 15, 1592-1596.
151. Golomb, M. [1968] "Approximation by periodic spline interpolants on uniform meshes," J. Approximation Theory, 1, 26-65.
152. Golumb, M., and H. Weinberger [1959] "Optimal approximation and error bounds," in On Numerical Approximation, R. E. Langer, Ed., University of Wisconsin Press, pp. 117-190.
153. Greville, T. N. E. [1944] "The general theory of osculatory interpolation," Trans. Actuar. Soc. Am., 45, 202-265.
154. Greville, T. N. E. [1964a] "Numerical procedures for interpolation by spline functions," SIAM J. Numer. Anal., 1, 53-68.
155. Greville, T. N. E. [1964b] "Interpolation by generalized spline functions," Math. Research Center Tech. Summary Report #476, U.S. Army, University of Wisconsin.
156. Greville, T. N. E. [1969a] Theory and Applications of Spline Functions, Ed., Academic Press, New York.
157. Greville, T. N. E. [1969b] "Introduction to spline functions," in Greville [1969aJ, pp. 1-35.
158. Hall, C. A. [1968] "On error bounds for spline interpolation," J. Approximation Theory, 1, 209-218.
159. Hardy, G. H., J. E. Littlewood, and G. Polya [1959] Inequalities, Cambridge University Press
160. Hedstrom, G. W., and R. S. Varga [1971] "Application of Besov spaces to spline approximation," J. Approximation Theory, 4,295-327.
161. Hildebrandt, F. B. [1956] Introduction to Numerical Analysis, McGraw-Hill, New York.
162. Holladay, J. C. [1957] "A smoothest curve approximation," Math. Tables Aids Computation, 11, 233-243.
163. Holmes, R. B. [1972] A Course on Optimization and Best Approximation, Lecture Notes in Mathematics, Springer, Heidelberg.
164. Ince, E. L. [1944] Ordinary Differential Equations, Dover, New York.
165. Isaacson, E., and H. B. Keller [1966] Analysis of Numerical Methods, Wiley, New York.
166. Ismagaov, R. S. [1974] "Diameter of sets in normal linear spaces and the approximation of functions by trigonometric polynomials," (Russian), Uspeki, Mat. Nauk, 29, 161-178 translated in Russian Math Surveys, 29, 179-186.
167. Jackson, D. [1930] The Theory of Approximation, AMS Vol. XI, Colloq. Publ. Providence, Rhode Island.
168. Jerome, J. W. [1973a] "On uniform approximation by certain generalized spline functions," J. Approximation Theory, 7, 143-154.
169. Jerome, J. W. [1973b] "Topics in multivariate approximation theory," in Lorentz [1973J, pp. 151-198.
170. p," Trans. Am. Math. Soc., 143, 363-371.
171. Jerome, J. W., and L. L. Schumaker [1971] "Local bases and computation of g-splines," Methoden und Varfahren der Math. Phys., 5, 171-199.
172. Jerome, J. W., and L. L. Schumaker [1973] "Characterizations of absolute continuity and essential boundedness for higher order derviatives," J. Math. Ana/y. Appl, 42, 452-465.
173. Jerome, J. W., and L. L. Schumaker [1974] "On the distance to a class of generalized splines," in Linear Operators and Approximation II, ISNM 25, Birkhauser Verlag, Basel, pp. 503-517.
174. Jerome, J. W., and L. L. Schumaker [1976] "Local support bases for a class of spline functions," J. Approximation Theory, 16, 16-27.
175. Jetter, K. [1976] "Nullstellen von Splines," in Schaback and Scherer [1976], pp. 291-304.
176. Johnen, H. [1972] "Inequalities connected with the moduli of smoothness," Mat. Vestnik, 9, 289-303.
177. Johnen, H., and K. Scherer [1976] "Direct and inverse theorems for best approximation by A-splines" in Bohmer, Meinardus, and Schempp [1976], pp. 116-131.
178. Johnen, H., and K. Scherer [1977] "On the equivalence of the K-functional and moduli of continuity and some applications" in Schempp and Zeller [1977], pp. 119-140.
179. Johnson, R. S. [1960] "On monosplines of least deviation:' Trans. Am. Math. Soc., 96, 458-477.
180. Jones, R. C., and L. A. Karlovitz [1970] "Equioscillation under nonuniqueness in the approximation of continuous functions:' J. Approximation Theory, 3, 138-145.
181. Kahane, J. P. [1961] Teoria Constructiva de Functiones, Course Notes, University de Buenos Aires.
182. Karlin, S. [1968] Total positivity, Volume I, Stanford University Press.
183. Karlin, S. [1969] "The fundamental theorem of algebra for monosplines satisfying certain boundary conditions and applications to optimal quadrature formulas," in Schoenberg [1969b], pp. 467-484.
184. Karlin, S. [1971] "Total positivity, interpolation by splines, and Green’s functions of differential operators:' 1. Approximation Theory, 4, 91-112.
185. Karlin, S. (1976a) "A global improvement theorem for polynomial monosplines," in Karlin, Michelli, Pinkus and Schoenberg, [1976], pp. 67-82.
186. Karlin, S. (1976b) "Oscillatory perfect splines and related extremal problems," in Karlin, Michelli, Pinkus, and Schoenberg [1976], pp. 371-460.
187. Karlin, S., and J. Karon [1968] "A variation diminishing generalized spline approximation method," J. Approximation Theory, 1, 255-268.
188. Karlin, S., and J. Karon [1970] "A remark on B-splines," J. Approximation Theory, 3, 455.
189. Karlin, S., and J. W. Lee [1970] "Poriodic boundary-value problems with cyclic totally positive Green’s functions with applications to periodic spline theory," J. Differential Equations, 8, 374-396.
190. Karlin, S., and C. Micchelli [1972] "The fundamental theorem of algebra for monosplines satisfying boundary conditions," Israel J. Math., II, 405-451.
191. Karlin, S., A. Micchelli, A. Pinkus, and I. J. Schoenberg [1976] Studies in Spline Functions and Approximation Theory, Academic Press, New York.
192. Karlin, S., and A. Pinkus [1976a] "Interpolation by splines with mixed boundary conditions" in Karlin, Michelli, Pinkus, and Schoenberg [1976], pp. 305-325.
193. Karlin, S., and A. Pinkus [1976b] "Divided differences and other non-linear existence problems at extremal points" in Karlin, Michelli, Pinkus, and Schoenberg (1976), pp. 327-352.
194. Karlin, S., and L. L. Schumaker [1967] "The fundamental theorem of algebra for Tchebycheffian monosplines," J. Analyse Math., 20, 233-270.
195. Karlin, S., and W. J. Studden [1966] Tchebycheff Systems: With Applications in Analysis and Statistics, Interscience, New York.
196. Karlin, S., and Z. Ziegler [1966] "Chebyshevian spline functions," SIAM J. Numer. Anal., 3, 514-543.
197. Karon, J. M. [1968] "The sign-regularity properties of a class of Green’s functions for ordinary differential equations and some related results," Dissertation, Stanford University.
198. Karon, J. M. [1969] "The sign-regularity properties of a class of Green’s functions for ordinary differential equations," J. Differential Equations, 6, 484-502.
199. Kashin, B. S. [1977a] "The widths of certain finite dimensional sets and classes of smooth functions," lzv. Akad. Nauk. SSSR. Ser. Math., 41, 334-335.
200. Kashin, B. S. [1977b] "Orders of the widths of certain classes of smooth functions," Uspeki. Math. Nauk., 32, 191-192.
201. Krein, M., and G. Finkelstein [1939] "Sur les fonctions de Green completement non-negatives des operateurs diffe rentiels ordinaires," Dok. Akad. Nauk SSSR, 24, 220-223.
202. Kolmogorov, A. N. [1936] "Annaherung von Funktionen einer gegebenen Funktionenklasse," Ann. of Math., 31 107-111.
203. Laurent, P. J. [1972] Approximation et Optimisation, Hermann, Paris.
204. Law, A. G., and B. N. Sahney [1976] Theory of Approximation with Applications, Eds., Academic Press, New York.
205. Lawson, C. L. [1964] "Characteristic properties of the segmented rational min-max approximation problem," Numer. Math., 6. 293-301.
206. LOfstrom, J. [1967] "Some theorems on interpolation spaces with applications to approximation in Lp," Math. Ann., 172, 176-196.
207. LOfstrom, J. [1970] "Besov spaces in theory of approximation," Ann. Mat. Pura. Appl., 85, 93-184.
208. Loginov, A. S. [1969] "Approximation of continuous functions by broken lines" (Russian), Mat. Zametki, 6, 149-160; see also Math. Notes, 6, 549-555.
209. Loginov, A. S. [1970] "Estimates for the approximation by polygonal lines of continuous functions of class HW," (Russian) Vestn;k Moskov Un;v. Ser. I. Mat. Meh., 25, 47-55.
210. Lorentz, G. G. [1953] Bernstein Polynomials, University of Toronto Press.
211. Lorentz, G. G. [1960] "Lower bounds for the degree of approximation," Trans. Am. Math. Soc., tn, 25-34.
212. Lorentz, G. G. [1966] Approximation of Functions, Holt, Rinehart and Winston, New York.
213. Lorentz, G. G. [1973] Approximation Theory, Ed. in cooperation with H. Berens, E. W. Cheney, and L. L. Schumaker, Academic Press, New York.
214. Lorentz, G. G. [1975] "Zeros of splines and Birkhofrs kernel," Math. Z., 142, 173-180.
215. Lorentz, G. G., C. K. Chui, and L. L. Schumaker [1976] Approximation Theory II, Eds., Academic Press, New York.
216. Louboutin, R. [1967a] "Sur une bonne partition de l’unite," in Glaeser [1967].
217. Louboutin, R. [1967b] Le Prolongateur de Whitney, Volume II, Publ. Sect. Math. Faculte des Sciences Rennes, France.
218. Love, A. E. H. [1944] A Treatise on the Mathematical Theory of Elasticity, Dover, New York.
219. Lyche, T. [1975] "Discrete polynomial spline approximation methods," Dissertation, University of Texas.
220. Lyche, T. [1976] "Discrete polynomial spline approximation methods," in Bohmer, Meinardus, and Schempp [1976], pp. 144-176.
221. Lyche, T. [1978] "A note on the condition numbers of the B-spline bases" J. Approximation Theory, 11, 202-205.
222. Lyche, T., and L. L. Schumaker [1973] "Computation of smoothing and interpolating natural splines via local bases," SIAM J. Numer. Anal., 10, 1027-1038.
223. Lyche, T. [1975] "LocaI spline approximation methods," J. Approximation Theory, 15, 294-325.
224. Lyche, T. [1976] "On determinants of spline functions," SFB Report # 107, University of Bonn, 1976.
225. Lyche, T., L. L. Schumaker, and K. Sepehrnoori [1980] "FORTRAN subroutines for computing smoothing and interpolating splines," Adv. Eng. Software 5 (1983), 2-5.
226. Lyche, T., and R. Winther [1979] "A stable recurrence relation for trigonometric B-splines," J. Approximation Theory, 15, 266-279.
227. Maclaren, D. H. [1958] "Formulas for fitting a spline curve through a set of points," Boeing Appl. Math. Report #2.
228. Makovoz, Vu. N. [1972] "A method of obtaining lower estimates for diameters of sets in Banach spaces," (Russian), Mat. Sb., 87, 136-146 translated in Math USSR Sb., 16, 139-146.
229. Malozemov, V. N. [1966] "On the deviation of broken lines," Vestnik Leningrad Univ., 21, 150-153.
230. Malozemov, V. N. [1967] "Polygonal interpolation" (Russian), Mat. Zametki, 1, 537-540, see also Math. Notes, 1, 355-357.
231. Mangasarian, O. L., and L. L. Schumaker [1971] "Discrete splines via mathematical programming," SIAM J. Control, 9, 174-183.
232. Mangasarian, O. L., and L. L. Schumaker [1973] "Best summation formulae and discrete splines," SIAM J. Numer. Anal., 10, 448-459.
233. Marsden, M. J. [1970] "An identity for spline functions with applications to variation-diminishing spline approximation," J. Approximation Theory, 3, 7-49.
234. Marsden, M. J., and I. J. Schoenberg [1966] "On variation diminishing spline approximation methods," Mathematica (Cluj), 8, 61-82.
235. Mayorov, V. E. [1975] "Discretization of the problem of diameters" (Russian) Uspeki Mat. Nauk, 30, 179-180.
236. McClure, D. [1975] "Nonlinear segmented function approximation and analysis of line patterns," Quart. Appl. Math., 33, 1-37.
237. Meinardus, G. [1967] Approximation of Functions; Theory and Numerical Methods, Springer-Verlag, Heidelberg.
238. Meinardus, G. [1974] "Bemerkung zur Theorie der B-Splines," in Bohmer, Meinardus, and Schemp [1974], pp. 165-175.
239. Meir, A., and A. Sharma [1969] "On uniform approximation by cubic splines," J. ApproxiWlQtion Theory, 2, 270-274.
240. Meir, A., and A. Sharma [1973] Spline Functions and Approximation theory, Eds., ISNM Vol. 21, BirkhauserVerlag, Basel.
241. Melkman, A. A. [1974a] "The Budan-Fourier theorem for splines," Israel J. Math., 19, 256-263.
242. Melkman, A. A. [1974b] "Interpolation by splines satisfying mixed boundary conditions," Israel J. Matk, 19, 369-381.
243. Melkman, A. A. [1977] "Splines with maximal zero sets," J. Math. Anal. Appl., 61, 739-751.
244. Meray, C [1884] "Observations sur la legitime de l’interpolation," Ann. Sci. Ecole Norm Sup., 1, 165-176.
245. Meray, C [1886] "Nouvelles examples d’interpolation illusoires," Bull Sci. Math., 20, 266-270.
246. Meyers, L. F., and A. Sard (1950a) "Best interpolation formulas," J. Math. and Phys., 29, 198-206.
247. Meyers, L. F., and A. Sard [1950b] "Best approximate integration formulas," J. Math. and Phys., 29, 118-123.
248. Micchelli, C. [1972] "The fundamental theorem of algebra for monosplines with multiplicities," in Linear Operators and Approximation, P. L. Butzer, J. Kahane, and B. S. Nagy, Eds., Basel, pp. 419-430.
249. Micchelli, C. A., and A. Pinkus [1977] "Moment theory for weak Tchebychev systems with applications to monosplines, quadrature formulae, and best one-sided L. approximation by spline functions with fixed knots," SIAM Math. Anal., 8, 206-230.
250. Micchelli, C., and T. J. Rivlin [1977] Optimal Estimation in Approximation Theory, Plenum Press, New York.
251. Milne-Thompson. L. M. [1960] The Calculus of Finite Differences, Macmillan, London.
252. Miihlbach, A. [1973] "‘A recurrence formula for generalized divided differences and some applications." J. Approximation Theory, 9. 165-172.
253. Munteanu. M. J.and L. L. Schumaker [1974] "‘Some multidimensional spline approximation methods.’" J. Approximation Theory. 10. 23-40.
254. Natanson, I. P. [1964] Constructive Function Theory, Ungar. New York.
255. Nemeth. A. B. [1966] "‘Transformations of the Chebyshev systems:’ Mathematica (Cluj), 8, 315-333.
256. Nemeth. A. B. [1969] "‘About the extension of the domain of the Chebycheff systems defined on intervals of the real axis:’ Mathematica (Cluj). II, 307-310.
257. Nemeth. A. B. [1975] "A geometrical approach to conjugate point classification for linear differential equations,''' Rec Anal. Nurn. Theor. Approx. 4. 137-152.
258. Nitsche. J. [1969a] "Sätze vom Jackson-Bemstein-Typ für die Approximation mit Spline-Funktionen." Math. Z. 109. 97-106.
259. Nemeth. A. B. [1969b] "Umkehrsätze für Spline-Approxinlationen:' Compositio Math. 21, 400-416.
260. Oswald, P. [1978] "Ungleichungen vom Jackson-typ fur die algebraische best Approximation in Lp '" J. Approximation Theory. 23, ] 13-136.
261. Pence, D. [1976] "Best approximation by constrained splines," Dissertation, Purdue University.
262. Peetre, J. [1963] A Theory of Interpolation of Normed Spaces, Lecture Notes, Brazilia.
263. Peetre, J. [1964] "Espaces d’interpolation, géneralisations, applications," Rend. Sem. Math. Fis. Milano, 34, 133-164.
264. Peterson, I. [1962] "On a piecewise polynomial approximation" (Russian), Eesti Nsv Tead. kad. Toimetised Fuus. Mat., 11, 24-32.
265. Phillips, G. M. [1968] "Estimate of the maximum error in best p<‘lynomial approximations," Comput. J., 11, 110-111.
266. Phillips, G. M. [1970] "Error estimates for best polynomial approximation," in Talbot [1970], 1-6.
267. Phillips, J. L., and R. J. Hanson [1974] "Gauss quadrature rules with B-spline weight functions," Math. Comp., 28, 666.
268. Pinkus, A. [1976] "A simple proof of the Hobby-Rice theorem," Proc. AMS, 60, 82-84.
269. Popov, V. A. [1974] "On the connection between rational and spline approximation," Compt. Rendus Acad Bulgarae Sci., 27, 623-626.
270. Popov, V. A. [1975a] "Direct and converse theorem for spline approximation with free knots," Bu/garicae Mathematicae Publ., 1, 218-224.
271. Popov, V. A. [1975b] "On approximation of absolutely continuous functions by splines," Mathematica (Cluj), 8, 1299-1301.
272. Popov, V. A., and G. Freud [1971] "Lower error bounds in the theory of spline functions," Studia Sci. Math. Hungar., 6, 387-391.
273. Popov, V. A., and B. H. Sendov [1970] "Classes characterized by best-possible approximation by spline functions," (Russian) Mat. Zametki, 8, 137-148; translated in Math. Notes, 8, 550-557.
274. Popov, V. A., and B. H. Sendov [1972] "On approximation of functions by spline functions and rational functions," in Constructive Function Theory, Bulgarian Academy of Sciences, pp. 89-92.
275. Popov, V. A., and J. Szabados [1974] "On a general localization theorem and some applications in the theory of rational approximation," Acta Math. Acad. Sci. Hungar., 25, 165-170.
276. Popoviciu, T. [1959] "Sur Ie reste dans certaines formules lineaires d’approximation de l’analyse," Mathematica (Cluj), 1, 95-142.
277. p-metric" (Russian), Kand. Dissertation, Moscow.
278. p," (Russian) Issedovaia po. Soor. Prob. Konstr. Teori Funksi, Moscow, pp. 64-69.
279. Prenter, P. M. [1975] Splines and Variational Methods, Wiley, New York.
280. Quade, W. and L. Collatz [1938] "Zur Interpolationstheorie der reellen periodischen Funktionen," Aka. Wiss. (Math-Phys. KI),30, 383-429.
281. Ralston, A. [1965] A First Course in Numerical Analysis. McGraw-Hill, New York.
282. Ream, N. [1961] "Note on approximation of curves by line segments," Math Comp., 15, 418-419.
283. Reddien, G. W., and L. L. Schumaker [1976] "On a collocation method for singular two-point boundary value problems," Numer. Math., 25, 427-432.
284. Reinsch, C. H. [1967] "Smoothing by spline functions," Numer. Math., 10, 177-183.
285. Rice, J. R. [1964] The Approximation of Functions, Vol. I, Linear Theory, Addison-Wesley, Reading, Massachusetts.
286. Rice, J. R. [1969a] "On the degree of convergence of nonlinear spline approximation," in Schoenberg [1969b], pp. 349-365.
287. Rice, J. R. [1969b] The Approximation of Functions, Vol. II., Nonlinear and Multivariate Theory, Addison-Wesley, Reading, Massachusetts.
288. Richards, F. [1972] "On the saturation class for spline functions," Proc. Am. Math. Soc., 33 (2), 471-476.
289. Richards, F. [1973] "Best bounds for the uniform periodic spline interpolation operator," J. Approximation Theory, 7, 302-317.
290. Richardson, C. H. [1954] An Introduction to the Calculus of Finite Differences, van Nostrand, New York.
291. Rivlin, T. J. [1969] An Introduction to Approximation of Functions, Blaisdell, Waltham, Massachusetts.
292. Rivlin, T. J. [1974] The Chebyshev Polynomials, Wiley, New York.
293. Runge, C. [1901] "Uber die Darstellung willkiirlicher Funktionen und die Interpolation zwischen aquidistanten Ordinaten," Z. Angew. Math. Phys., 46, 224-243.
294. Runge, C. [1904] Theorie und Praxis der Reihen, Teubner, Leibniz.
295. Runge, C. [1931] "Uber imperische Funktionen," Math. Phys., 46, 224-243.
296. Rutman, M. A. [1965] "Integral representation of functions forming a Markov series," (Russian) Dokl. Akad. Nauk SSSR, 164, 989-992.
297. Sacks, J., and D. Ylvisaker [1966] "Designs for regression with correlated errors," Ann. Math. Stat., 37, 66-89.
298. Sacks, J., and D. Ylvisaker [1968] "Designs for regression with correlated errors: many parameters," Ann. Math. Stat., 39, 49-69.
299. Sacks, J., and D. Ylvisaker [1969] "Statistical designs and integral approximation," Proc. 12th Bienn. Sem. Canad. Math. Congr., pp. 115-136.
300. Sacks, J., and D. Ylvisaker [1970] "Designs for regression with correlated errors, III," Ann. Math. Stat., 41, 2057-2074.
301. Sard, A. [1949] "Best approximate integration formulas, best approximation formulas," Am. J.Math., 71, 80-91.
302. Sard, A. [1963] Linear Approximation, AMS Survey Vol. 9, Providence, Rhode Island.
303. Sard, A., and S. Weintraub [1971] A Book of Splines, Wiley, New York.
304. Schaback, R. [1973] "Spezielle rationale Splinefunktionen," J. Approximation Theory, 7, 281-292.
305. Schaback, R., and K. Scherer [1976] Approximation Theory, Eds., Springer Lecture Notes 556, Heidelberg.
306. Schempp, W., and K. Zeller [1977] Constructive Theory of Functions of Several Variables, Eds., Springer-Verlag Lecture Notes 571, Heidelberg.
307. Scherer, K. [1970a] "Uber die beste Approximation von LP-Funktionen durch Splines," in Proc. of Conference on Constructive Function Theory, Varna, pp. 277-286.
308. Scherer, K. [1970b] "On the best approximation of continuous functions by splines," SIAM J. Numer. Anal., 7, 418-423.
309. Scherer, K. [1974a] "Characterization of generalized Lipschitz classes by best approximation with splines," SIAM J. Numer. Anal., 11, 283-304.
310. Scherer, K. [1974b] "Stetigkeitsmoduli und beste Approximation durch polynomiale Splines," in Bohmer, Meinardus, and Schempp [1974], pp. 289-302.
311. Scherer, K. [1976] "Some inverse theorems for best approximation by A-splines," in Lorentz, Chui, and Schumaker [1976], pp. 549-555.
312. Scherer, K. [1977] "Optimal degree of approximation by splines," in Micchelli and Rivlin [1977], pp. 139-158.
313. Scherer, K., and L. L. Schumaker [1980] "A dual basis for Tchebycheffian B-splines and applications," J. Approximation Theory 29 (1980), 151-169.
314. Schmidt, E., P. Lancaster, and D. Watkins [1975] "Bases of splines associated with constant coefficient differential operators," SIAM J. Numer. Anal., 12, 630-645.
315. Schoenberg, I. J. [1946a] "Contributions to the problem of approximation of equidistant data by analytic functions, Part A: On the problem of smoothing of graduation, a first class of analytic approximation formulae," Quart. Appl. Math., 4, 45-99.
316. Schoenberg, I. J. [1946b] "Constributions to the problem of approximation of equidistant data by analytic functions, Part B: On the problem of osculatory interpolation, a second class of analytic approximation formulae." Quart. Appl. Math., 4, 112-141.
317. Schoenberg, I. J. [1958] "Spline functions, convex curves and mechanical quadrature," Bull. Am. Math. Soc., 64, 352-357.
318. Schoenberg, I. J. [1964a] "On interpolation by spline functions and its minimal properties," Int. Sere Numer. Anal., S, 109-129.
319. Schoenberg, I. J. [1964b] "On trigonometric spline interpolation," J. Math. Mech. 13, 795-826.
320. Schoenberg, I. J. [1964c] "Spline interpolation and the higher derivatives," Proc. Nat. Acad. Sci. U.S.A., 51,24-28.
321. Schoenberg, I. J. [1967] "On spline functions," in Inequalities, O. Shisha, Ed. Academic Press, New York, pp. 255-291.
322. Schoenberg, I. J. [1968] "On the Ahlberg-Nilson extension of spline interpolation: the g-splines and their optimal properties," J. Math. Anal. Appl., 21, 207-231.
323. Schoenberg, I. J. [1969a] "Cardinal interpolation and spline functions," J. Approximation Theory, 2, 167-206.
324. Schoenberg, I. J. [1969b] Approximations with Special Emphasis on Spline functions, Ed., Academic Press, New York.
325. Schoenberg, I. J. [1971] "The perfect B-splines and a time optimal control problem," Israel J. Math., 10, 261-274.
326. Schoenberg, I. J. [1972a] "Cardinal interpolation and spline functions. 11., Interpolation of data of power growth," J. Approximation Theory, 6, 404-420.
327. Schoenberg, I. J. [1972b] "Cardinal interpolation and spline functions, IV. The exponential Euler splines", in ISNM Volume 20 Birkhauser, pp. 382-404.
328. Schoenberg, I. J. [1973] Cardinal Spline Interpolation, CBMS 12, SIAM, Philadelphia.
329. Schoenberg, I. J., and A. Whitney [1949] "Sur la positivite des determinants de translations des fonctions de frequence de Polya avec une application a une probleme d’interpolation par les fonctions ‘spline’," Compt. Rend., 228, 1996-1998.
330. Schoenberg, I. J., and A. Whitney [1953] "On Polya frequency functions III. The positivity of translation determinants with application to the interpolation problem by spline curves," Trans. Am. Math. Soc., 74, 246-259.
331. Scholz, R. [1974] "Abschatzungen linearer Durchmesser in Sobolev und Besov Raumen," Manuscripta Math., 11, 1-14.
332. Schultz, M. H. [1969a] "Approximation theory of multivariate spline functions in Sobolev spaces," SIAM J. Numer. Anal., 6, 570-582.
333. Schultz, M. H. [1969b] "Loo-multivariate approximation theory," SIAM J. Numer. Anal., 6, 161-183.
334. Schultz, M. H. [1973a] "Error bounds for a bivariate interpolation scheme," J. Approximation Theory, 8, 189-194.
335. Schultz, M. H. [1973b] Spline Analysis, Prentice-Hall, Englewood Cliffs, New Jersey.
336. Schultz, M. H., and R. S. Varga [1967] "L-splines," Numer. Math., 10, 345-369.
337. Schumaker, L. L. [1966] "On some approximation problems involving Tchebycheff systems and spline functions," Dissertation, Stanford University.
338. Schumaker, L. L. [1968a] "Uniform approximation by Tchebycheffian spline functions," J. Math. Meck, 18, 369-377.
339. Schumaker, L. L. [1968b] "Uniform approximation by Chebyshev spline functions II. Free Knots," SIAM J. Numer. Anal., 5, 647-656.
340. Schumaker, L. L. [1969] "On the smoothness of best spline approximation: J. Approximation Theory, 2, 410-418.
341. Schumaker, L. L. [1973] "Constructive aspects of discrete polynomial spline functions," in Lorentz [1973], pp. 469-476.
342. Schumaker, L. L. [1976a] "On Tchebycheffian spline functions," J. Approximation Theory, 18, 278-303.
343. Schumaker, L. L. [1976b] "Zeros of spline functions and applications," J. Approximation Theory, 18, 152-168.
344. Schumaker, L. L. [1976c] "Toward a constructive theory of generalized spline functions," in Bohmer, Meinardus, and Schempp [1976], pp. 265-331.
345. Schumaker, L. L. [1978] "Lower bounds for spline approximation," Banach Center Publ. 4, pp. 213-223.
346. Schwartz, J. T. [1969] Nonlinear Functional Analysis, Gordon and Breach, New York.
347. Schweikert, D. G. [1966a] "The spline in tension (hyperbolic spline) and the reduction of extraneous inflection points," Dissertation, Brown University.
348. Schweikert, D. G. [1966b] "An interpolation curve using a spline in tension," J. Math. and Phys., 45, 312-317.
349. Schwerdtfeger, H. [1960] "Notes on numerical analysis, II. Interpolation and curve fitting by sectionally linear functions," Canad. Math. Bull., 3, 41-57.
350. Schwerdtfeger, H. [1961] "Notes on numerical analysis III. Further remarks on sectionally linear functions," Canad. Math. Bull., 4, 53-55.
351. Segethova, J. [1972] "Numerical construction of the hill functions," SIAM J. Numer. Anal., 9, 199-204.
352. Sendov, B. L., and V. A. Popov [1970a] "Approximation of curves by piecewise polynomial curves," Dokl. Bulg. Akad. Nauk, 23, 639-643.
353. Sendov, B. L., and V. A. Popov (1970b) "The approximation of spline functions," C. R. Acad. Bulgare Sci., 23, 755-758.
354. Shah, J. M. [1970] "Two-dimensional polynomial splines," Numer. Matk, 15, 1-14.
355. Shapiro, H. S. [1971] Topics in Approximation Theory, Springer-Verlag, Lecture Notes 187, Heidelberg.
356. Sharma, A., and A. Meir [1966] "Degree of approximation of spline interpolation," J. Math. Mech., 15, 759-768.
357. Shisha, O. [1973] "A characterization of functions having Zygmund’s property," J. Approximation Theory,9,395-397.
358. Shisha, O. [1974a] "Characterization of smoothness properties of functions by means of their degree of approximation by splines," J. Approximation Theory, 12, 365-371.
359. Shisha, O. [1974b] "On the degree of approximation by step functions," J. Approximation Theory, 12, 435-436.
360. Shisha, O. [1975] "On saturation with splines," J. Approximation Theory, 13, 491-494.
361. Smith, K. [1970] "Formulas to represent functions by their derivatives," Math. Annal., 188, 53-77.
362. Smoluk, A. [1964] "On the approximation with piecewise functions" (Polish), Zeszyty Nauk. Wyz. Szkol. Ekon. Wroclawiu, 21, 123-157.
363. Sobolev, S. L. [1963] Applications of Functional Analysis in Mathematical Physics, Am. Math. Soc., Providence, Rhode Island.
364. Solomiak, M. Z., and V. M. Tihomirov [1967] "Geometric characteristics of the imbedding of the classes Wα p in C" (Russian) Invest. Vozoo. Mat., 10, 76-82.
365. Sommer, M. [1976] "Weak-Chebychev spaces and splines," Dissertation, Erlangen.
366. Sommer, M. [1979] "Continuous selections of the metric projection for 1-Chebychev spaces," J. Approximation Theory, 26, 46-53.
367. Sommer, M. [1980a] "Nonexistence of continuous selections of the metric projection for a class of Weak Chebychev systems," Trans. Am. Math. Soc., 260, 403-410.
368. Sommer, M. [1980b] "Characterization of continuous selections of the metric projection for generalized spline functions," SIAM J. Math. Anal., 11, 23-40.
369. Sommer, M. [1980c] "Weak Chebyshev spaces and Best L.-approximation", in press.
370. Sommer, M., and H. Strauss [1977] "Eigenschaften von schwach Tschebyscheffschen Raumen," J. Approximation Theory, 21, 257-268.
371. Spath, H. [1969] "Exponential spline interpolation," Computing, 4, 225-233.
372. Sommer, M. [1971] "Two-dimensional exponential splines," Computing, 7, 364-369.
373. Sommer, M. [1973] Spline-Algorithon zur Konstruktion glatter Kuroen and Flachen, R. Oldenburg Verlag, Munchen, Germany. English translation by W. D. Hoskins and H. W. Sager, Spline Algorithms for Curves and surfaces, Utilitas Mathematical Publ. Inc., Winnipeg, Manitoba, 1974.
374. Stechkin, S. D., and Vu. N. Subbotin [1978] Splines in Numerical Mathematics (Russian), Izd. Nauka, Moscow.
375. Stockenberg, B. [1977a] "On the number of zeros of functions in a weak Tchebycheff-space," Math. Z., 156,49-57.
376. Stockenberg, B. [1977b] "Subspaces of weak and oriented Tchebyshev-spaces," Manuscripta Math., 20, 401-407.
377. Stone, H. [1961] "Approximation of curves by line segments," Math. Comp., 15, 40-47.
378. p, metric," (Russian) Mat. Zametki, 5, 31-37; see also, Math. Notes, 5, 21-25.
379. k), 0
380. k), 0
381. Strang, G., and G. J. Fix [1973] An Analysis of the Finite Element Method, Prentice Hall, Englewood Cliffs, New Jersey.
382. Subbotin, Yu. N. [1967] "Best approximation of a class of functions by another class" (Russian), Mat. Zametki, 2, 495-504; see also Math Notes, 2, 792-797.
383. P by m-order splines" (Russian), Dokl Akad. Nauk SSSR, 195; see also Soviet Math. Dokl. 11, 1626-1628.
384. Subbotin, Yu. N. [I970b] "Diameter of class W’L in L(0,2Φ) and spline function approximation" (Russian), Mat. Zametki, 7, 43-52; see also Math Notes, 7, 256-260.
385. Subbotin, Yu. N. [1971] "Approximation by spline functions and estimates of diameters" (Russian), Proc. Steklov. Inst. Math., 109, 39-67.
386. Subbotin, Yu. N., and N. I. Chemykh [1970] "Order of the best spline approximations of some classes of functions," Math Notes, 7, 20-26.
387. 2n + 2-1) bounds on some spline interpolation errors," Bull. Am. Math. Soc., 74, 1072-1078.
388. kf; h)] bounds on some spline interpolation errors," Dissertation, New York University.
389. Swartz, B., and R. S. Varga (1972) "Error bounds for spline and L-spline interpolation," J. Approximation Theory, 6, 6-49.
390. Szego, G. [1939] Orthogonal Polynomials, AMS Colloq. Publ. Vol. 23, Providence, Rhode Island.
391. Talbot, A. [1970] Approximation Theory, Ed., Academic Press, London.
392. Theilheimer, F., and W. Starkweather [1961] "The fairing of ship lines on a high-speed computer," Numerical Tables Aids Computation, IS, 338-355.
393. Tihomirov, V. M. [1965] "Some problems of approximation theory," Soviet Math. Dokl., 6, 202-205.
394. Tihomirov, V. M. [1969] "Best methods of approximation and interpolation of differentiable functions in the space C[-1, I]" (Russian), Mat. Sb., SO, 290-304; see also Math. USSR-Sb,9, 275-289.
395. Tihomirov, V. M. [1970] "Some problems in approximation theory" (Russian), Dissertation, Moscow University, 1970.
396. Tihomirov, V. M. [1971] "Some problems in approximation theory" (Russian), Mat. Zametki, 9, 593-607; see also Math Notes, 9, 343-350.
397. Timan, A. F. [1963] Theory of Approximation of Functions of a Real Variable, MacMillan, New York.
398. Todd, J. [1963] Introduction to the Constructive Theory of Functions, Birkhauser, Basel.
399. Varga, R. S. [1969] "Error bounds for spline interpolation," in Schoenberg [1969b], pp. 367-388.
400. van Rooij and F. Schurer [1974] "A bibliography on spline functions," in Bohmer, Meinardus and Schempp [1974], pp. 315-415.
401. Volkov, V. I. [1958] "Some properties of Chebyshev systems" (Russian), Ucen. Zap. Ka/inin. Gos. Pede Inst., 26, 41-48.
402. Walsh, J. L. [1960] Interpolation and Approximation by Rational Functions in the Complex Domain, AMS Colloq. Pub. 20, Providence, Rhode Island.
403. Walsh, J. L., J. H. Ahlberg, and E. N. Nilson [1962] "Best approximation properties of the spline fit," J. Math. Mech., 11, 225-234.
404. Werner, H. [1962] "Ein Satz tiber diskrete Tschebyscheff-Approximation bei gebrochen linearen Funktionen," Numer. Math., 4, 154-157.
405. Werner, H. [1974] "Tschebyscheff-Approximation mit einer Klasse rationaler Spline-Funktionen," J. Approximation Theory, 10, 74-92.
406. Werner, H. [1976] "Approximation by regular splines with free knots" in Lorentz, Chui, and Schumaker (1976), pp. 567-573.
407. Whitney, H. [1957]..".On functions with n-th bounded differences," J. Math. Pure Appl, 36, 60-95.
408. Young, J. D. [1968] "Numerical applications of hyperbolic spline functions," The Logistics Review, 4, 17-22.
409. Young, J. D. [1969] "Generalization of segmented spline fitting of third order," The Logistics Review, 5,33-40.
410. Zalik, R. A. [1975] "Existence of Tchebycheff extensions," J. Math. Anal. Applic., 51, 68-75.
411. Zalik, R. A. [1977a] "Integral representation of Tchebycheff systems," PacIfic J. Math., 68, 553-568.
412. Zalik, R. A. [1977b] "On transforming a Tchebycheff system into a complete Tchebycheff system," J. Approximation Theory, 20, 220-222.
413. Zielke, R. [1972] "A remark on periodic Tchebyshev systems," Manuscripta Math., 7, 325-329.
414. Zielke, R. [1973] "On transforming a Tchebyshev-system into a Markov-system," J. Approximation Theory, 9, 357-363.
415. Zielke, R. [1974] "Alternation properties of Tchebycheff systems and the existence of adjoined functions," J. Approximation Theory, 10, 172-184.
416. Zielke, R. [1975] "Tchebycheff systems that cannot be transferred into a Markov system," Manuscripta Math., 17, 67-71.
417. Zielke, R. [1979] Discontinuous Cebysev Systems, Springer-Verlag Lecture Notes 707, Heidelberg.
418. Zwart, P. B. [1973] "Multi-variate splines with non-degenerate partitions," SIAM J. Numer. Anal., 10, 665-673.
419. Zygmund, A. [1959] Trigonometric Series, Volumes I and II, Cambridge University Press.
420. Barry, P. J. [Bar90] de Boor-Fix functionals and polar forms, Comput. Aided Geom. Design 7 (1990), 425-430.
421. Barry, P. J. [Bar92b] Symmetrizing multiaffine polynomials, in Mathematical Methods in Computer Aided Geometric Design II, T. Lyche and L. L. Schumaker (eds.), New York, Academic Press, 1992, 1-7.
422. Barry, P. J. [Bar93] An introduction to blossoming, in Knot Insertion and Deletion Algorithms for B-spline Modeling, R. N. Goldman and T. Lyche (eds.), Philadelphia, SIAM, 1993, 1-10.
423. Barry, P. J. [Bar96] de Boor-Fix dual functionals and algorithms for Tchebycheffian B-spline curves, Constr. Approx. 12 (1996), 385-408.
424. Barry, P., N. Dyn, R. Goldman, and C. A. Micchelli [BarDGM91] Polynomial identities for piecewise polynomial spaces determined by connection matrices, Aequat. Mathem. 42 (1991), 123-136.
425. Barry, P. J. and R. N. Goldman [BarG88a] A recursive proof of Boehm’s knot insertion algorithm, Computer-Aided Design 5 (1988), 173-175.
426. Barry, P. J. and R. N. Goldman [BarG88b] A recursive proof of an identity for B-spline degree elevation, Comput. Aided Geom. Design 5 (1988), 173-175.
427. Barry, P. J. and R. N. Goldman [BarG93a] Knot insertion algorithms, in Knot Insertion and Deletion Algorithms for B-spline Modeling, R. N. Goldman and T. Lyche (eds.), Philadelphia, SIAM, 1993, 89-133.
428. Barry, P. J. and R. N. Goldman [BarG93b] Factored knot insertion, in Knot Insertion and Deletion Algorithms for B-spline Modeling, R. N. Goldman and T. Lyche (eds.), Philadelphia, SIAM, 1993, 65-88.
429. Barry, P. J. and R. N. Goldman [BarG93c] Algorithms for progressive curves: Extending B-spline and blossoming techniques to the monomial, power, and Newton dual bases, in Knot Insertion and Deletion Algorithms for B-spline Modeling, R. N. Goldman and T. Lyche (eds.), Philadelphia, SIAM, 1993, 11-63.
430. Barry, P. J., R. N. Goldman, and C. A. Micchelli [BarGM93] Knot insertion algorithms for piecewise polynomial spaces determined by connection matrices, Advances in Comp. Math. 1 (1993), 139-171.
431. Barry, P. J. and R.-F. Zhu [BarZ92] Another knot insertion algorithm for B-spline curves, Comput. Aided Geom. Design 9 (1992), 175-183.
432. Barsky, B. A. [Bars81] The beta spline: a local representation based on shape parameters and fundamental geometric measures, dissertation, Univ. Utah, 1981.
433. Barsky, B. A. and J. C. Beatty [BarsB83] Local control of bias and tension in Beta splines, ACM Trans. on Graphics 2 (1983), 109-134.
434. Barsky, B. A. and T. D. DeRose [BarsD85] The β 2-spline: a special case of the β-spline curve and surface representation, IEEE Comp. Graph. Appl. 5(9) (1985), 46-58.
435. Barsky, B. A. and T. D. DeRose [BarsD90] Geometric continuity of parametric curves: Three equivalent characterizations, Comp. Graphics and Applics. 9 (1990), 60-68.
436. Bartels, R. H. and J. C. Beatty [BartB97] Connection-matrix splines by divided differences, in Curves and Surfaces in Geometric Design, A. LeMéhauté, C. Rabut, and L. L. Schumaker (eds.), Nashville TN, Vanderbilt University Press, 1997, 9-16.
437. Bartels, R. H., J. C. Beatty, and B. A. Barsky [BartBB87] An Introduction to Splines for Use in Computer Graphics & Geometric Modeling, Los Altos, CA, Morgan Kaufmann Publ., 1987.
438. Beatson, R. K. [Bea81] Convex approximation by splines, SIAM J. Math. Anal. 12 (1981), 549-559.
439. Beatson, R. K. [Bea82a] Restricted range approximation by splines and variational inequalities, SIAM J. Numer. Anal. 19 (1982), 372-380.
440. Beatson, R. K. [Bea82b] Monotone and convex approximation by splines: error estimates and a curve fitting algorithm, SIAM J. Numer. Anal. 19 (1982), 1278-1285.
441. Beatson, R. K. and D. Leviatan [BeaL83] On comonotone approximation, Canad. Math. Bull. 26 (1983), 220-224.
442. Bezhaev, A. Y. and V. A. Vasilenko [BezV01] Variational Theory of Splines, New York, Kluwer/Plenum, 2001.
443. Bister, D. and H. Prautzsch [BisP97] Anewapproach to Tchebycheffian B-splines, in Curves and Surfaces in Geometric Design, A. LeMéhauté, C. Rabut, and L. L. Schumaker (eds.), Nashville TN, Vanderbilt University Press, 1997, 35-41.
444. Bittner, K. [Bit06] Biorthogonal spline wavelets on the interval, in Wavelets and Splines, G. Chen and M. J. Lai (eds.), Brentwood, Nashboro Press, 2006, 93-104.
445. Boehm, W. [Boe80] Inserting new knots into B-spline curves, Computer-Aided Design 12(4) (1980), 199-201.
446. Boehm, W. [Boe85] On the efficiency of knot insertion algorithms, Comput. Aided Geom. Design 2(1-3) (1985), 141-143.
447. Boehm, W. and H. Prautzsch [BoeP85] The insertion algorithm, Computer-Aided Design 17(2) (1985), 58-59.
448. Bojanov, B. D. [Boj80] Perfect splines of least uniform deviations, Analysis Mathematica 6 (1980), 185-197.
449. Bojanov, B. D. [Boj88] B-splines with Birkhoff knots, Constr. Approx. 4 (1988), 147-156.
450. Bojanov, B. D. [Boj02] Markov-type inequalities for polynomials and splines, in Approximation Theory X: Abstract and Classical Analysis, C. K. Chui, L. L. Schumaker, and J. Stöckler (eds.), Nashville, Vanderbilt University Press, 2002, 31-90.
451. Bojanov, B. D., H. A. Hakopian, and A. A. Sahakian [BojHS93] Spline Functions and Multivariate Interpolations, Dordrecht, The Netherlands, Kluwer Academic Publishers, 1993.
452. Bojanov, B. and N. Naidenov [BojN02] Exact Markov-type inequalities for oscillating perfect splines, Constr. Approx. 18 (2002), 37-59.
453. Boor, C. de [Boo88] The condition of the B-spline basis for polynomials, SIAM J. Numer. Anal. 25 (1988), 148-152.
454. Boor, C. de [Boo90] The exact condition of the B-spline basis may be hard to determine, J. Approx. Theory 60 (1990), 344-359.
455. Boor, C. de [Boo92] Approximation order without quasi-interpolants, in Approximation Theory VII, E. W. Cheney, C. Chui, and L. L. Schumaker (eds.), New York, Academic Press, 1992, 1-18.
456. Boor, C. de [Boo97] The multiplicity of a spline zero, Annals of Numerical Mathematics 4 (1997), 229-238.
457. Boor, C. de [Boo01] A Practical Guide to Splines, Revised Edition, New York, xviii + 346p, Springer-Verlag, 2001.
458. Boor, C. de and R. DeVore [BooD85]Ageometric proof of total positivity for spline interpolation, Math. Comp. 45(172) (1985), 497-504.
459. Boor, C. de and K. Höllig [BooH87] B-splines without divided differences, in Geometric Modeling: Algorithms and New Trends, G. E. Farin (ed.), Philadelphia, SIAM Publications, 1987, 21-27.
460. Boor, C. de and A. Pinkus [BooP03] The B-spline recurrence relations of Chakalov and of Popoviciu, J. Approx. Theory 124(1) (2003), 115-123.
461. Braess, D. and N. Dyn [BraD82] On the uniqueness of monosplines and perfect splines of least L1-and L 2-norm, J. Analyse Math. 41 (1982), 217-233.
462. Buhmann, M. and C. A. Micchelli [BuhM92] Spline prewavelets for non-uniform knots, Numer. Math. 61 (1992), 455-474.
463. Carlson, B.C. [Car91] B-splines, hypergeometric functions, and Dirichlet averages, J. Approx. Theory 67 (1991), 311-325.
464. Carnicer, J. M. and J. M. Peña [CarnP93] A Marsden’s type identity for periodic trigonometric splines, J. Approx. Theory 75(3) (1993), 248-265.
465. Carnicer, J. M. and J. M. Peña [CarnP94] Totally positive bases for shape preserving curve design and optimality of B-splines, Comput. Aided Geom. Design 11 (1994), 635-656.
466. Casteljau, P. de [Cas85] Formes à Poles, Paris, Hermes, 1985.
467. Casteljau, P. de [Cas93] Polar forms for curve and surface modeling as used at Citröen, in Fundamental Developments of Computer-Aided Geometric Modeling, Les Piegl (ed.), London, Academic Press, 1993, 1-12.
468. Chen, D.-R. [Che94] Perfect splines with boundary conditions of least norm, J. Approx. Theory 77 (1994), 191-201.
469. Chen, H.-L. [Chen81] Complex spline functions, Sci. Sinica 24 (1981), 160-169.
470. Chen, H.-L. [Chen83] The zeros of rational splines and complex splines, J. Approx. Theory 39 (1983), 308-319.
471. Cho, O. and M.-J. Lai [ChoL06] A class of compactly supported orthonormal B-spline wavelets, in Wavelets and Splines, G. Chen and M. J. Lai (eds.), Brentwood, Nashboro Press, 2006, 123-151.
472. Chui, C. K. [Chu88] Multivariate Splines, Philadelphia, CBMS-NSF Reg. Conf. Series in Appl. Math., vol. 54, SIAM, 1988.
473. Chui, C. K. [Chu92] An Introduction to Wavelets, Boston, Academic Press, 1992.
474. Chui, C. K. and J. M. DeVilliers [ChuD98] Spline-wavelets with arbitrary knots on a bounded interval: orthogonal decomposition and computational algorithms, Commun. Appl. Anal. 2 (1998), 457-486.
475. p approximation by monotone splines, SIAM J. Math. Anal. 11 (1980), 436-447.
476. Chui, C. K. and E. Quak [ChuQ92] Wavelets on a bounded interval, in Numerical Methods in Approximation Theory, ISNM 105, D. Braess, L.L. Schumaker (eds.), Basel, Birkhäuser, 1992, 53-75.
477. Chui, C. K. and Jian-Zhong Wang [ChuW91] A cardinal spline approach to wavelets, Proc. Amer. Math. Soc. 113(3) (1991), 785-793.
478. Chui, C. K. and Jian-Zhong Wang [ChuW92a] On compactly supported spline wavelets and a duality principle, Trans. Amer. Math. Soc. 330 (1992), 903-915.
479. Chui, C. K. and Jian-Zhong Wang [ChuW92b] A general framework of compactly supported splines and wavelets, J. Approx. Theory 71(3) (1992), 263-304.
480. Chui, C. K. and Jian-Zhong Wang [ChuW93] An analysis of cardinal spline-wavelets, J. Approx. Theory 72(1) (1993), 54-68.
481. Chui, C. K. and Jian-Zhong Wang [ChuW94] A study of compactly supported scaling functions and wavelets, in Wavelets, Images, and Surface Fitting, P.-J. Laurent, A. LeMéhauté, and L. L. Schumaker (eds.), Wellesley MA, A. K. Peters, 1994, 121-140.
482. Ciesielski, Z. and T. Figiel [CieF82a] Spline approximation and Besov spaces on compact manifolds, Studia Math. 75 (1982), 13-36.
483. Ciesielski, Z. and T. Figiel [CieF82b] Spline bases in classical function spaces on compact c∞ manifolds, Studia Math. 76 (1982), 1-58.
484. Ciesielski, Z. and T. Figiel [CieF83] Spline bases in classical function spaces on compact C∞ manifolds, Part II, Studia Math. 76 (1983), 95-136.
485. Cohen, A., I. Daubechies, and J.-C. Feauveau [CohDF92] Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math. XLV (1992), 485-560.
486. Cohen, E., T. Lyche, and K. Mørken [CohLM85] Knot line refinement algorithms for tensor product B-spline surfaces, Comput. Aided Geom. Design 2 (1985), 133-139.
487. Cohen, E., T. Lyche, and R. Riesenfeld [CohLR80] Discrete b-splines and subdivision techniques in computer-aided geometric design and computer graphics, Comp. Graphics and Image Proc. 14 (1980), 87-111.
488. Cohen, E., T. Lyche, and L. L. Schumaker [CohLS85] Algorithms for degree-raising of splines, ACM Trans. on Graphics 4 (1985), 171-181.
489. Cohen, E., T. Lyche, and L. L. Schumaker [CohLS86] Degree raising for splines, J. Approx. Theory 46 (1986), 170-181.
490. Cohen, E., R. E. Riesenfeld, and G. Elber [CohRE01] Geometric Modeling with Splines, Natick, MA, AK Peters, 2001.
491. Cohen, E. and L. L. Schumaker [CohS85] Rates of convergence of control polygons, Comput. Aided Geom. Design 2 (1985), 229-235.
492. Costantini, P. [Cos97] Variable degree polynomial splines, in Curves and Surfaces in Geometric Design, A. LeMéhauté, C. Rabut, and L. L. Schumaker (eds.), Nashville TN, Vanderbilt University Press, 1997, 85-94.
493. Dahmen, W. [Dah86] Subdivision algorithms converge quadratically, J. Comput. Appl. Math. 16 (1986), 145-158.
494. Dahmen, W., A. Kunoth, and K. Urban [DahKU99] Biorthogonal spline wavelets on the interval-stability and moment conditions, Appl. Comput. Harmon. Anal. 6 (1999), 132-196.
495. Davydov, O. V. [Dav95] A class of weak Chebyshev spaces and characterization of best approximations, J. Approx. Theory 81 (1995), 250-259.
496. p, 0 < p < ∞, Constr. Approx. 12(3) (1996), 409-422.
497. p (0 < p < 1), J. Approx. Theory 75(1) (1993), 79-84.
498. DeVore, R. A., D. Leviatan, and I. A. Shevchuk [DevLS97] Approximation of monotone functions: a counter example, in Curves and Surfaces in Geometric Design, A. LeMéhauté, C. Rabut, and L. L. Schumaker (eds.), Nashville TN, Vanderbilt University Press, 1997, 95-102.
499. p (0 < p < 1), Constr. Approx. 8 (1992), 187-201.
500. DeVore, R. A. and X. M. Yu [DevY85] Pointwise estimates for monotone polynomial approximation, Constr. Approx. 1 (1985), 323-331.
501. Dierckx, P. [Die93] Curve and Surface Fitting with Splines, Oxford, England, Monographs on Numerical Analysis, Oxford University Press, 1993.
502. Dierckx, P. and B. Tytgat [DieT89] Inserting new knots into β spline curves, in Mathematical Methods in Computer Aided Geometric Design, T. Lyche and L. L. Schumaker (eds.), New York, Academic Press, 1989, 195-205.
503. Ditzian, Z. and V. Totik [DitT87] Moduli of smoothness, New York, Springer-Verlag, 1987.
504. Donovan, G. C., J. S. Geronimo, and D. P. Hardin [DonGH96] Intertwining multiresolution analyses and the construction of piecewise-polynomial wavelets, SIAM J. Math. Anal. 27 (1996), 1791-1815.
505. Dyn, N. [Dyn83] Perfect splines of minimum norm for monotone norms and norms induced by innerproducts, with applications to tensor product approximations and n-widths of integral operators, J. Approx. Theory 38 (1983), 105-138.
506. Dyn, N. and A. Ron [DynR88] Recurrence relations for Tchebycheffian B-splines, J. Analyse Math. 51 (1988), 118-138.
507. Farin, G. (ed.) [Far87] Geometric Modelling, Philadelphia, SIAM, 1987.
508. Farin, G. (ed.) [Far90] Curves and Surfaces for Computer Aided Geometric Design, Second Edition, NY, Academic Press, 1990.
509. Farin, G. (ed.) [Far95] NURBS Curves and Surfaces: from Projective Geometry to Practical Use, Wellesley, MA, AKPeters, 1995.
510. Goldman, R. N. [Gol90] Blossoming and knot insertion algorithms for B-spline curves, Comput. Aided Geom. Design 7(1-4) (1990), 69-81.
511. Goldman, R. N. [Gol95] Identities for the B-spline basis functions, in Graphics Gems, Vol. V, Alan W. Paeth (ed.), NY, Academic Press, 1995, 163-167.
512. Goldman, R. N. and P. J. Barry [GolB92]Wonderful triangle: a simple, unified, algorithmic approach to change of basis procedures in computer aided geometric design, in Mathematical Methods in Computer Aided Geometric Design II, T. Lyche and L. L. Schumaker (eds.), NewYork, Academic Press, 1992, 297-320.
513. Goldman, R. N. and B. Barsky [GolBar89] On β-continuous functions and their application to the construction of geometrically continuous curves and surfaces, in Mathematical Methods in Computer Aided Geometric Design, T. Lyche and L. L. Schumaker (eds.), New York, Academic Press, 1989, 299-311.
514. Goodman, T. N. T. [Goo85] Properties of Beta-splines, J. Approx. Theory 44 (1985), 132-153.
515. Goodman, T. N. T. [Goo94] New bounds on the zeros of spline functions, J. Approx. Theory 76(1) (1994), 123-130.
516. Goodman, T. N. T. [Goo03] A class of orthogonal refinable functions and wavelets, Constr. Approx. 19(4) (2003), 525-540.
517. Goodman, T. N. T. and S. L. Lee [GooL78] Another extremal property of perfect splines, Proc. Amer. Math. Soc. 70(2) (1978), 129-135.
518. Goodman, T. N. T. and S. L. Lee [GooL82] The Budan-Fourier Theorem and Hermite-Birkhoff spline interpolation, Trans. Amer. Math. Soc. 271(2) (1982), 451-467.
519. Goodman, T. N. T. and S. L. Lee [GooL83] B-splines on the circle and trigonometric B-splines, in Approximation Theory and Spline Functions, S. P. Singh, J. H. W. Burry, and B. Watson (eds.), Dordrecht, Reidel, 1984, 297-325.
520. Goodman, T. N. T. and S. L. Lee [GooL84] Interpolatory and variation-diminishing properties of generalized B-splines, Proc. Edinburgh Math. Soc., Sect A 96(3-4) (1984), 249-259.
521. Goodman, T. N. T. and S. L. Lee [GooL94] Interpolatory Hermite spline wavelets, J. Approx. Theory 78 (1994), 174-189.
522. Goodman, T. N. T. and K. Unsworth [GooU85] Generation of β-spline curves using a recurrence relation, in Fundamental Algorithms for Computer Graphics, R. A. Earnshaw (ed.), Berlin, Springer, 1985, 325-357.
523. Gonsor, D. and M. Neamtu [GonN94] Non-polynomial polar forms, in Curves and Surfaces in Geometric Design, P.-J. Laurent, A. LeMéhauté, and L. L. Schumaker (eds.), Wellesley MA, A. K. Peters, 1994, 193-200.
524. Höllig, K. [Hol00] Stability of the B-spline basis via knot insertion, Comput. Aided Geom. Design 17 (2000), 447-450.
525. Hoschek, J. and D. Lasser [HosL93] Fundamentals of Computer Aided Geometric Design, Boston MA, A. K. Peters, 1993.
526. Hu, Y. K. [Hu93] Convex approximation by quadratic splines, J. Approx. Theory 74 (1993), 69-82.
527. p[-1, 1], 0 < p < ∞, J. Approx. Theory 86 (1996), 320-334.
528. Hu, Y. K., K. A. Kopotun, and X. M. Yu [HuKY97] Constrained approximation in Sobolev spaces, Canad. J. Math. 49 (1997), 74-99.
529. Hu, Y. K., K. A. Kopotun, and X. M. Yu [HuKY99]Weak copositive and intertwining approximation, J. Approx. Theory 96 (1999), 213-236.
530. Hu, Y., D. Leviatan, and X. M. Yu [HuLY94] Convex polynomial and spline approximation in c[-1, 1], Constr. Approx. 10(1) (1994), 31-64.
531. Hu, Y., D. Leviatan, and X. M. Yu [HuLY95] Copositive polynomial and spline approximation, J. Approx. Theory 80(2) (1995), 204-218.
532. Huang, Q.-X., S-M. Hu, and R. R. Martin [HuaHM05] Fast degree elevation and knot insertion for B-spline curves, Comput. Aided Geom. Design 22 (2005), 183-197.
533. Ivanov, K. G. and B. Popov [IvaP96] On convex approximation by quadratic splines, J. Approx. Theory 85 (1996), 110-114.
534. Jena, M. K., P. Shunmugaraj, and P. C. Das [JenSD02] A subdivision algorithm for trigonometric spline curves, Comput. Aided Geom. Design 19 (2002), 71-88.
535. Jia, R. Q. [Jia81] On local linear functionals for L-splines, J. Approx. Theory 33 (1981), 96-110.
536. Jia, R. Q. [Jia82a] B-splines associated with a linear differential operator, Numer. Math. Sinica 4 (1982), 128-138.
537. Jia, R. Q. [Jia82b] B-splines associated with a linear differential operator II, Numer. Math. Sinica 4 (1982), 264-271.
538. Jia, R. Q. [Jia83] Total positivity of the discrete spline collocation matrix, J. Approx. Theory 39 (1983), 11-23.
539. Jia, R. Q. [Jia06] Stable bases of spline wavelets on the interval, in Wavelets and Splines, G. Chen and M. J. Lai (eds.), Brentwood, Nashboro Press, 2006, 243-259.
540. Joe, B. [Joe87] Discrete β-splines, Proc. SIGGRAPH’87 21 (1987), 137-144.
541. Joe, B. [Joe90] Knot insertion for beta-spline curves and surfaces, ACM Trans. on Graphics 9(2) (1990), 41-65.
542. Koch, P. E. [Koc85] Jackson-type theorems for trigonometric polynomials and splines, in Alfred Haar Memorial Conference, J. Szabados and K. Tandori (eds.), Amsterdam, North-Holland, 1987, 485-493.
543. Koch, P. E. and T. Lyche [KocL89a] Error estimates for best approximation by piecewise trigonometric and hyperbolic polynomials, Det Kongelige Norske Vitenskapers Selskap, Skrifter 2 (1989), 73-86.
544. Koch, P. E. and T. Lyche [KocL89b] Exponential B-splines in tension, in Approximation Theory VI, C. Chui, L. Schumaker, and J. Ward (eds.), New York, Academic Press, 1989, 361-364.
545. Koch, P. E. and T. Lyche [KocL91] Construction of exponential tension B-spline of arbitrary order, in Curves and Surfaces, P.-J. Laurent, A. LeMéhauté, and L. L. Schumaker (eds.), New York, Academic Press, 1991, 255-258.
546. Koch, P. E., T. Lyche, M. Neamtu, and L. L. Schumaker [KocLNS95] Control curves and knot insertion for trigonometric splines, Advances in Comp. Math. 3 (1995), 405-424.
547. Kopotun, K. A. [Kop94] Pointwise and uniform estimates for convex approximation of functions by algebraic polynomials, Constr. Approx. 10(2) (1994), 153-178.
548. Kopotun, K. A. [Kop95a] Coconvex polynomial approximation of twice differentiable functions, J. Approx. Theory 83 (1995), 141-156.
549. p, 0 < p < ∞ (quasi)norm, in Approximation Theory VIII, Vol. 1: Approximation and Interpolation, C. K. Chui and L. L. Schumaker (eds.), Singapore, World Scientific Publishing Co., Inc., 1995, 295-302.
550. Kopotun, K. A. [Kop01] Whitney theorem of interpolatory type for k-monotone functions, Constr. Approx. 17(2) (2001), 307-317.
551. Kopotun, K. A. [Kop07] Univariate splines: equivalence of moduli of smoothness and applications, Math. Comp., to appear.
552. p, Proc. Amer. Math. Soc. 134 (2006), 2037-2047.
553. Kopotun, K., D. Leviatan, and I. A. Shevchuk [KopLS06] Coconvex approximation in the uniform norm: the final frontier, Acta Math. Hungar. 110 (2006), 117-151.
554. Kopotun, K. and A. Y. Shadrin [KopSh03] On k-monotone approximation by free knot splines, SIAM J. Math. Anal. 34 (2003), 901-924.
555. Kounchev, O. and H. Render [KouR02] Wavelet analysis of cardinal L-splines and construction of multivariate prewavelets, in Approximation Theory X: Splines, Wavelets, and Applications, C. K. Chui, L. L. Schumaker, and J. Stöckler (eds.), Nashville, Vanderbilt University Press, 2002, 333-353.
556. Krystadt, U. J. [Kry84] On the Schoenberg Whitney theorem for L-splines (Norwegian), Diplom thesis, Oslo, 1984.
557. Kvasov, Boris I. [Kva00] Methods of Shape Preserving Spline Approximation, Singapore, World Scientific Publishing Co Pte Ltd, 2000.
558. Kvasov, B. I. and P. Sattayatha [KvaS97] Generalized tension B-splines, in Curves and Surfaces in Geometric Design, A. LeMéhauté, C. Rabut, and L. L. Schumaker (eds.), Nashville TN, Vanderbilt University Press, 1997, 247-254.
559. Kvasov, B. I. and P. Sattayatha [KvaS99] GB-splines of arbitrary order, J. Comput. Appl. Math. 104 (1999), 63-88.
560. Lai, M.-J. and K. Nam [LaiN06] Tight wavelet frames and bounded domains, in Wavelets and Splines, G. Chen and M. J. Lai (eds.), Brentwood, Nashboro Press, 2006, 314-327.
561. Lai, M.-J. and L. L. Schumaker [LaiS07] Spline Functions on Triangulations, Cambridge, Cambridge University Press, 2007.
562. Lane, J. M. and R. F. Riesenfeld [LanR83] A geometric proof for the variation diminishing property of B-spline approximation, J. Approx. Theory 37 (1983), 1-4.
563. Laurent, P. J., M.-L. Mazure, and V. T. Maxim [LauMM97] Chebyshev splines and shape parameters, Numer. Algorithms 15 (1997), 373-383.
564. Laurent, P.-J., M.-L. Mazure, and G. Morin [LauMMo97] Shape effects with polynomial Chebyshev splines, in Curves and Surfaces in Geometric Design, A. LeMéhauté, C. Rabut, and L. L. Schumaker (eds.), Nashville TN, Vanderbilt University Press, 1997, 255-262.
565. Lee, E. T. Y. [Lee82] A simplified B-spline computation routine, Computing 29 (1982), 365-371.
566. Lee, E. T. Y. [Lee85] Some remarks concerning B-splines, Comput. Aided Geom. Design 2 (1985), 307-311.
567. Lee, E. T. Y. [Lee86] Comments on some B-spline algorithms, Computing 36 (1986), 229-238.
568. Lee, E. T. Y. [Lee89a] Yet another proof of knot insertion, Comput. Aided Geom. Design 6 (1989), 83-84.
569. Lee, E. T. Y. [Lee89b] A note on blossoming, Comput. Aided Geom. Design 6 (1989), 359-362.
570. Lee, E. T. Y. [Lee94a] Remarks on an identity related to degree elevation, Comput. Aided Geom. Design 11 (1994), 109-111.
571. Lee, E. T. Y. [Lee94b] Computing a chain of blossoms, with application to product of splines, Comput. Aided Geom. Design 11 (1994), 597-620.
572. Lee, E. T. Y. [Lee96] Marsden’s identity, Comput. Aided Geom. Design 13 (1996), 287-305.
573. Lee, S. L., C. A. Micchelli, A. Sharma, and P. W. Smith [LeeMSS83] Some properties of periodic B-spline collocation matrices, Proc. Edinburgh Math. Soc.Sect. A 94(3-4) (1983), 235-246.
574. Lempel, A. and G. Seroussi [LemS92] Systematic derivation of spline bases, Comput. Aided Geom. Design 9 (1992), 349-363.
575. Leviatan, D. [Lev88] Monotone and comonotone approximation revisted, J. Approx. Theory 53 (1988), 1-16.
576. pnorm, SIAM J. Math. Anal. 13 (1982), 866-874.
577. Leviatan, D. [LevM82b] Comonotone approximation by splines of piecewise monotone functions, J. Approx. Theory 35 (1982), 364-369.
578. Leviatan, D. and A. Y. Shadrin [LevSha97]Onmonotone and convex approximation by splines with free knots, Annals of Numerical Mathematics 4 (1997), 415-434.
579. Leviatan, D. and I. A. Shevchuk [LevShe97] Some positive results and counterexamples in comonotone approximation, J. Approx. Theory 89(2) (1997), 195-206.
580. Leviatan, D. and I. A. Shevchuk [LevShe98] Nearly comonotone approximation, J. Approx. Theory 95 (1998), 53-81.
581. Leviatan, D. and I. A. Shevchuk [LevShe00] Nearly comonotone approximation. II., Acta Math. Acad. Sci. Hungar. 66 (2000), 115-135.
582. Leviatan, D. and I. A. Shevchuk [LevShe02a] Coconvex approximation, J. Approx. Theory 118 (2002), 20-65.
583. Leviatan, D. and I. A. Shevchuk [LevShe02b] Nearly coconvex approximation, Serdica Math. J. 28 (2002), 361-378.
584. Leviatan, D. and I. A. Shevchuk [LevShe03] Coconvex polynomial approximation, J. Approx. Theory 121 (2003), 100-118.
585. Li, Y. [Li85] On the recurrence relations for B-splines defined by certain L-splines, J. Approx. Theory 43 (1985), 359-369.
586. Liu, W. [Liu97] A simple, efficient degree raising algorithm for B-spline curves, Comput. Aided Geom. Design 14 (1997), 693-698.
587. Lü, Y. G. X. [Lu02] Uniform hyperbolic polynomial B-spline curves, Comput. Aided Geom. Design 19 (2002), 379-393.
588. Lutterkort, D. and J. Peters [LutP00] Linear envelopes for uniform B-spline curves, in Curve and Surface Design: Saint-Malo 99, P.-J. Laurent, P. Sablonni`ere, and L. L. Schumaker (eds.), Nashville TN, Vanderbilt University Press, 2000, 239-246.
589. Lutterkort, D. and J. Peters [LutP01] Tight linear envelopes for splines, Numer. Math. 89 (2001), 735-748.
590. Lyche, T. [Lyc78] A note on the condition numbers of the B-spline bases, J. Approx. Theory 22 (1978), 202-205.
591. Lyche, T. [Lyc85] A recurrence relation for Chebyshevian B-splines, Constr. Approx. 1 (1985), 155-173.
592. Lyche, T. [Lyc86] Chebyshevian B-splines and knot insertion, in Approximation Theory V, C. Chui, L. Schumaker, and J. Ward (eds.), New York, Academic Press, 1986, 455-458.
593. Lyche, T. [Lyc88] Note on the Oslo algorithm, Computer-Aided Design 20(6) (1988), 353-355.
594. Lyche, T. [Lyc89] Condition numbers for B-splines, in Numerical Analysis 1989, D. F. Griffiths and G. A. Watson (eds.), Essex, Longman Scientific and Technical, 1989, 189-192.
595. Lyche, T. [Lyc90] Discrete B-splines and conversion problems, in Computation of Curves and Surfaces, W. Dahmen, M. Gasca, and C. Micchelli (eds.), Dordrecht, Netherlands, Kluwer, 1990, 117-134.
596. Lyche, T. and K. Mørken [LycM86] Making the Oslo algorithm more efficient, SIAM J. Numer. Anal. 23 (1986), 663-675.
597. Lyche, T. and K. Mørken [LycM92] Spline-wavelets of minimal support, in Numerical Methods in Approximation Theory, ISNM 105, D. Braess, L.L. Schumaker (eds.), Basel, Birkhäuser, 1992, 177-194.
598. Lyche, T. and K. Mørken [LycM93] How much can the size of the B-spline coefficients be reduced by inserting one knot?, in Knot Insertion and Deletion Algorithms for B-spline Modeling, R. N. Goldman and T. Lyche (eds.), Philadelphia, SIAM, 1993, 155-178.
599. Lyche, T. and K. Mørken [LycM99] The sensitivity of a spline function to perturbations of the knots, BIT 39 (1999), 305-322.
600. Lyche, T., K. Mørken, and E. Quak [LycMQ01] Theory and algorithms for non-uniform spline wavelets, in Multivariate Approximation and Applications, A. Pinkus, D. Leviatan, N. Dyn, and D. Levin (eds.), Cambridge, Cambridge University Press, 2001, 152-187.
601. Lyche, T. and L. L. Schumaker [LycS94] L-spline wavelets, in Wavelets: Theory, Algorithms, and Applications, C. Chui, L. Montefusco, and L. Puccio (eds.), New York, Academic Press, 1994, 197-212.
602. Lyche, T. and L. L. Schumaker [LycS96] Total positivity properties of LB-splines, in Total Positivity and its Applications, M. Gasca, C. A. Micchelli (eds.), Dordrecht, Kluwer, 1996, 35-46.
603. Lyche, T., L. L. Schumaker, and S. Stanley [LycSS98] Quasi-interpolants based on trigonometric splines, J. Approx. Theory 95 (1998), 280-309.
604. Mainar, E. and J. M. Peña [MaiP00] Knot insertion and totally positive systems, J. Approx. Theory 104(1) (2000), 45-76.
605. Mason, J. C., G. Rodriguez, and S. Seatzu [MasRS93] Orthogonal splines based on B-splines-with applications to least squares, smoothing and regularization problems, Numer. Algorithms 5 (1993), 25-40.
606. Mathur, K. K. and A. Sharma [MatS79] Discrete polynomials splines on the circle, Acta Math. Acad. Sci. Hungar. 33(1-2) (1979), 143-153.
607. Mazure, M.-L. [Maz01] Four properties to characterize Chebyshev blossoms, Constr. Approx. 17(3) (2001), 319-334.
608. Mazure, M.-L. and P.-J. Laurent [MazL96] Marsden identity, blossoming and de Boor-Fix formula, in Advanced Topics in Multivariate Approximation, F. Fontanella, K. Jetter, and P.-J. Laurent (eds.), Singapore, World Scientific Publishing Co., 1996, 227-242.
609. Meinardus, G., H. ter Morsche, and G. Walz [MeiMW95] On the Chebyshev norm of polynomial B-splines, J. Approx. Theory 82(1) (1995), 99-122.
610. Melkman, A. A. [Mel96] Another proof of the total positivity of the discrete spline collocation matrix, J. Approx. Theory 84(3) (1996), 265-273.
611. Mørken, K. [Mor84] On two topics in spline theory: Discrete splines and the equioscillating spline, Master’s thesis, Oslo, 1984.
612. Mørken, K. [Mor89] Contributions to the theory and applications of splines, dissertation, Univ. of Oslo, 1989.
613. Mørken, K. [Mor91] Some identities for products and degree raising of splines, Constr. Approx. 7 (1991), 195-208.
614. Mørken, K. [Mor96] On total positivity of the discrete spline collocation matrix, J. Approx. Theory 84(3) (1996), 247-264.
615. Nairn, D., J. Peters, and D. Lutterkort [NaiPL99] Sharp, quantitative bounds on the distance between a polynomial and its Bézier control polygon, Comput. Aided Geom. Design 16 (1999), 613-633.
616. Nielson, G. M. [Nie74] Some piecewise polynomial alternatives to splines under tension, in Computer Aided Geometric Design, R. E. Barnhill and R. F. Riesenfeld (eds.), New York, Academic Press, 1974, 209-235.
617. Nürnberger, G. [Nur89] Approximation by Spline Functions, Berlin, Springer-Verlag, 1989.
618. Nürnberger, G., L. L. Schumaker, M. Sommer, and H. Strauss [NurSSS84] Generalized Tchebycheffian Splines, SIAM J. Numer. Anal. 15 (1984), 790-804.
619. Nürnberger, G., L. L. Schumaker, M. Sommer, and H. Strauss [NurSSS85] Approximation by generalized spline functions, J. Math. Anal. Appl. 108 (1985), 466-494.
620. Peters, J. and X. Wu [PetW03] On the optimality of piecewise linear max-norm enclosures based on slefes, in Curve and Surface Design: Saint-Malo 2002, T. Lyche, M.-L. Mazure, and L. L. Schumaker (eds.), Brentwood TN, Nashboro Press, 2003, 335-344.
621. Peters, J. and X. Wu [PetW04] SLEVEs for planar spline curves, Comput. Aided Geom. Design 21 (2004), 615-635.
622. Petrov, P. P. [Petr96] Shape preserving approximation by free knot splines, East J. Approx. 2(1) (1996), 41-48.
623. Piegl, L. and W. Tiller [PieT84] Software-engineering approach to degree elevation of B-spline curves, Computer-Aided Design 26 (1984), 17-28.
624. Piegl, L. and W. Tiller [PieT95] The NURBS Book, Heidelberg, Springer-Verlag, 1995.
625. Pinkus, A. [Pin78] Some extremal properties of perfect splines and the pointwise Landau problem on the finite interval, J. Approx. Theory 23 (1978), 37-64.
626. Popoviciu, T. [Pop34] Sur le prolongement des fonctions convexes d’ordre superieur, Bull. Math. Soc. Roumaine des Sc. 36 (1934), 75-108.
627. Pottmann, H. [Pot93] The geometry of Tchebycheffian splines, Comput. Aided Geom. Design 10 (1993), 181-210.
628. Pottmann, H. and M. G. Wagner [PotW94] Helix splines as an example of affine Tchebycheffian splines, Advances in Comp. Math. 2 (1994), 123-142.
629. Prautzsch, H. [Pra84a] A short proof of the Oslo algorithm, Comput. Aided Geom. Design 1 (1984), 95-96.
630. Prautzsch, H. [Pra84b] Degree elevation of B-spline curves, Comput. Aided Geom. Design 1 (1984), 193-198.
631. Prautzsch, H., W. Boehm, and M. Paluszny [PraBP02] Bézier and B-spline Techniques, Berlin, Springer, 2002.
632. Prautzsch, H. and L. Kobbelt [PraK94] Convergence of subdivision and degree elevation, Advances in Comp. Math. 2 (1994), 143-154.
633. Prautzsch, H. and B. Piper [PraP91] A fast algorithm to raise the degree of spline curves, Comput. Aided Geom. Design 8 (1991), 253-265.
634. Prymak, A. V. [Pry02] Three-convex approximation by quadratic splines with arbitrary fixed knots, East J. Approx. 8 (2002), 185-196.
635. Prymak, A. V. [Pry05] Shape-preserving smoothing of 3-convex splines of degree four, Ukrainian Math. J. 57 (2005), 331-339.
636. Quak, E. and N. Weyrich [QuaW94a] Decomposition and reconstruction algorithms for splinewavelets on a bounded interval, Appl. Comput. Harmonic Anal. 1 (1994), 217-231.
637. Quak, E. and N. Weyrich [QuaW94b] Decomposition and reconstruction algorithms for bivariate spline wavelets on the unit square, in Wavelets, Images, and Surface Fitting, P.-J. Laurent, A. LeMéhauté, and L. L. Schumaker (eds.), Wellesley MA, A. K. Peters, 1994, 419-428.
638. Qu, R. and J. A. Gregory [QuG92] A subdivision algorithm for non-uniform B-splines, in Approximation Theory, Spline Functions and Applications, S. P. Singh (ed.), Dordrecht, Netherlands, Kluwer, 1992, 423-436.
639. Ramshaw, L. [Ram87] Blossoming: a connect-the-dots approach to splines, Techn. Rep., Digital Systems Research Center, Palo Alto, 1987.
640. Ramshaw, L. [Ram88] Béziers and B-splines as multiaffine maps, in Theoretical Foundations of Computer Graphics and CAD, NATO Advanced Study Institute Series, R. A. Earnshaw (ed.), Heidelberg, Springer-Verlag, 1988, 757-776.
641. Ramshaw, L. [Ram89] Blossoms are polar forms, Comput. Aided Geom. Design 6(4) (1989), 323-358.
642. Reif, U. [Rei00] Best bounds on the approximation of polynomials and splines by their control structure, Comput. Aided Geom. Design 17 (2000), 579-589.
643. Riesenfeld, R. [Rie73] Applications of B-spline approximation to geometric problems of computer-aided design, dissertation, Syracuse Univ., 1973.
644. Rogina, M. [Rog97]Aknot insertion algorithm for weighted cubic splines, in Curves and Surfaces in Geometric Design, A. LeMéhauté, C. Rabut, and L. L. Schumaker (eds.), Nashville TN, Vanderbilt University Press, 1997, 387-394.
645. Rogina, M. and T. Bosner [RogB00] On calculating with lower order Chebyshev splines, in Curve and Surface Design: Saint-Malo 99, P.-J. Laurent, P. Sablonni`ere, and L. L. Schumaker (eds.), Nashville TN, Vanderbilt University Press, 2000, 343-352.
646. Rogina, M. and T. Bosner [RogB03] A de Boor type algorithm for tension splines, in Curve and Surface Fitting: Saint-Malo 2002, A. Cohen, J.-L. Merrien, and L. L. Schumaker (eds.), Brentwood TN, Nashboro Press, 2003, 343-352.
647. Ropela, S. [Rop76a] Spline bases in Besov spaces, Bull. Acad. Polonaise Sci. 24 (1976), 319-325.
648. Ropela, S. [Rop76b] Decomposition lemma and unconditional spline bases, Bull. Acad. Polonaise Sci. 24 (1976), 467-470.
649. Romani, L. and M. A. Sabin [RomS04] The conversion matrix between uniform B-spline and Bézier representations, Comput. Aided Geom. Design 21 (2004), 549-560.
650. Sakai, M. and A. Togashi [SakT90] On hyperbolic and trigonometric B-splines on equally spaced knots, Rep. Fac. Sci. Kagoshima Univ. Math. Phys. 23 (1990), 13-21.
651. Sakai, M. and R. A. Usmani [SakU84] Exponential quadratic splines, Proc. Japan Acad. Ser. A Math. Sci. 60 (1984), 26-29.
652. Sakai, M. and R. A. Usmani [SakU86] On exponential splines, J. Approx. Theory 47 (1986), 122-131.
653. Santoro, E. [San92] Some probabilistic properties of B-splines and an application to dimensional tolerance, Computer-Aided Design 24(11) (1992), 619-622.
654. Scherer, K. [Sche94] The condition number of B-splines and related constants, in Open Problems in Approximation Theory, B. Bojanov (ed.), Singapore, SCT Publishing, 1994, 180-191.
655. Scherer, K. and A. Y. Shadrin [ScheSh96] New upper bound for the B-spline basis condition number, East J. Approx. 2(3) (1996), 331-342.
656. Scherer, K. and A. Y. Shadrin [ScheSh99] New upper bound for the B-spline basis condition number. II. A proof of de Boor’s 2k-conjecture, J. Approx. Theory 99(2) (1999), 217-229.
657. Schmeltz, G. [Schm94] Variation diminution and blossoming for curves and surfaces, in Curves and Surfaces in Geometric Design, P.-J. Laurent, A. LeMéhauté, and L. L. Schumaker (eds.), Wellesley MA, A. K. Peters, 1994, 427-434.
658. Schneider, F.-J. [Schn93] Interpolation, Approximation und Konvertierung mit rationalen B-Splines, dissertation, Darmstadt, 1993.
659. Schumaker, L. L. [Schu82] On recursions for generalized splines, J. Approx. Theory 36 (1982), 16-31.
660. Schumaker, L. L. [Schu83] On hyperbolic splines, J. Approx. Theory 38 (1983), 144-166.
661. Schumaker, L. L. [Schu84] Splines and computer-aided design, Delft Progress Rpt. 9 (1984), 292-304.
662. Seidel, H.-P. [Sei88] Knot insertion from a blossoming point of view, Comput. Aided Geom. Design 5 (1988), 81-86.
663. Seidel, H.-P. [Sei89] A new multi-affine approach to B-splines, Comput. Aided Geom. Design 6 (1989), 23-32.
664. Seidel, H.-P. [Sei91] Universal splines and geometric continuity, in Curves and Surfaces, P.-J. Laurent, A. LeMéhauté, and L. L. Schumaker (eds.), New York, Academic Press, 1991, 437-444.
665. Seidel, H.-P. [Sei93a] An introduction to polar forms, IEEE Comp. Graph. Appl. 13(1) (1993), 38-46.
666. Seidel, H.-P. [Sei93b] Polar forms for geometrically continuous splines of arbitrary degree, ACM Trans. on Graphics 12 (1993), 1-34.
667. Shadrin, A. Y. [Sha83] Monotone approximation of functions by trigonometric polynomials, Math. Notes 34 (1983), 669-675.
668. p-metric, Anal. Math. 12 (1986), 175-184.
669. Shadrin, A. Y. [Sha87] Jackson’s type theorems for monotone approximation of functions by trigonometric polynomials, Math. Notes 42 (1987), 933-944.
670. Shevchuk, I. A. [She97] One construction of cubic convex spline, in Approximation and optimization, Vol. I (Cluj-Napoca, 1996), Transilvania, Cluj-Napoca, 1997, 357-368.
671. Sommer, M. and H. Strauss [SomS88]Weak Descartes systems in generalized spline spaces, Constr. Approx. 4 (1988), 133-145.
672. Stephanus, Y. and R. N. Goldman [SteG92] Blossoming Marsden’s identity, Comput. Aided Geom. Design 9 (1992), 73-84.
673. Švedov, A. S. [Sve81] Orders of coapproximation of functions by algebraic polynomials, Mat. Zametki 29 (1981), 117-130.
674. Tschakaloff, L. [Tsc38] Eine Integraldarstellung des Newtonschen Differenzenquotienten und ihre Anwendungen, Annuaire Univ. Sofia, Fiz. Mat. Fakultet 34 (1938), 395-405.
675. Utreras, F. [Utr82] Convergence rates for monotone cubic spline interpolation, J. Approx. Theory 36 (1982), 86-90.
676. Varah, J. M. [Var77] On the condition number of local bases for piecewise cubic polynomials, Math. Comp. 31(137) (1977), 37-44.
677. Vasilenko, V. A. [Vas83] Spline Functions: Theory, Algorithms, Programs (Russian), Novosibirsk, Akad. Nauk SSSR, Novosibirsk Computing Center, 1983.
678. Vermeulen, A. H., R. H. Bartels, and G. R. Heppler [VerBH92] Integrating Products of B-Splines, SIAM J. Sci. Statist. Comput. 13(4) (1992), 1025-1038.
679. Vesprille, K. J. [Ves75] Computer-aided design applications of the rational B-spline approximation form, dissertation, Syracuse Univ., 1975.
680. Walz, G. [Wal89] Remarks on exponential splines, in particular a contour integral representation of exponential B-splines, Math. Methods in the Applied Sciences 11 (1989), 821-827.
681. Walz, G. [Wal90] B-splines im Komplexen, Complex Variables Theory Appl. 15 (1990), 90-105.
682. Walz, G. [Wal91] Spline-Funktionen im Komplexen, Mannheim, B.I.-Wissenschafts-verlag, 1991.
683. Walz, G. [Wal97] Identities for trigonometric B-splines, with an application to curve design, BIT 37 (1997), 189-201.
684. Wang, J. [Wan06] On spline wavelets, in Wavelets and Splines, G. Chen and M. J. Lai (eds.), Brentwood, Nashboro Press, 2006, 456-483.
685. Wang, G., Q. Chen, and M. Zhou [WanCZ04] NUAT B-spline curves, Comput. Aided Geom. Design 21 (2004), 193-205.
686. Wang, R.-H. [Wang01] Multivariate Spline Functions and their Applications, Boston, Kluwer Academic Publ., 2001.
687. p spaces, Approx. Theory Appl. 3 (1987), 72-83.
688. Yu, X. M. and S. P. Zhou [YuZ94] On monotone spline approximation, SIAM J. Math. Anal. 25 (1994), 1227-1239.
689. Zavialov, Y. S., B. I. Kvasov, and V. L. Miroshnichenko [ZavKM80] Methods of Spline-Functions (Russian), Moscow, Nauka, 1980.
690. Zhang, J. W. [Zha96] C-curves an extension of cubic curves, Comput. Aided Geom. Design 13 (1996), 199-217.
691. Zhang, J. W. [Zha97] Two different forms of C-B splines, Comput. Aided Geom. Design 14 (1997), 31-41.