An introduction to numerical methods and analysis

An Introduction to Numerical Methods and Analysis

Volumn , Issue , 2021, Pages 1-650

  Epperson, James F ^a  

^a NONE

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EID: 85121487599     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9781119604754     Document Type: Book

References (177)

1. Acton, Forman S.; Numerical Methods That Work, Mathematical Association of America, Washington, DC, 1990 (originally published by Harper & Row, 1970).
2. Allen, Myron B., and Isaacson, Eli L.; Numerical Analysis for Applied Science, John Wiley & Sons, Inc., New York, 1998.
3. Asaithambi, A. S.; Numerical Analysis, Theory and Practice, Saunders College Publishing, Fort Worth, TX, 1995.
4. Atkinson, Kendall; An Introduction to Numerical Analysis, JohnWiley & Sons, Inc., New York, 1989 (2nd Edition).
5. Atkinson, Kendall; Elementary Numerical Analysis, John Wiley & Sons, Inc., New York, 1993 (2nd Edition).
6. Bradie, Brian, A Friendly Introduction to Numerical Analyisis, Pearson Prentice Hall, Upper Saddle River, NJ, 2006.
7. Burden, Richard, and Faires, J. Douglas; Numerical Analysis, Brooks/Cole, Pacific Grove, CA, 2012 (9th Edition).
8. Cheney, Ward, and Kincaid, David; Numerical Mathematics and Computing, Brooks/Cole Publishing, Pacific Grove, CA, 2012 (7th Edition).
9. Conte, S.D., and de Boor, Carl; Elementary Numerical Analysis, McGraw-Hill, New York, 1980 (3rd Edition).
10. Dahlquist, Germund, and Bjorck, Ake; Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ, 1974.
11. Dyson, George; Turing’s Cathedral, Vintage, New York, 2012.
12. Faires, J. Douglas and Burden, Richard; Numerical Methods, Brooks/Cole, Pacific Grove, CA, 2012 (4th Edition).
13. Godfrey, Michael (ed.), von Neumann, John; “First draft of a report on the EDVAC, " IEEE Annals on the History of Computing, vol. 15, no. 4, pp. 27-75, 1993. Available online at http://web.mit.edu/STS.035/www/PDFs/edvac.pdf.
14. Goldstine, Herman H.; The Computer: From Pascal to von Neumann, Princeton University Press, Princeton, NJ, 1980.
15. Goldstine, Herman H.; Numerical Analysis from the 16th to the 19th Century, Springer-Verlag, New York, 1977.
16. Grandine, Thomas; The Numerical Methods Programming Projects Book, Oxford Science Publications, Oxford, UK, 1970.
17. Gregory, John, and Redmond, Don; Introduction to Numerical Analysis, Jones & Bartlett Publishers, Boston, 1994.
18. Gustafsson, Bertil; Scientific Computation: A Historical Perspective, Springer, 2018.
19. Hill, Christian; Learning Scientific Programming with Python, Cambridge University Press, Cambridge, 2015.
20. Hodges, Andrew; Alan Turing: The Enigma: The Book That Inspired the Film The Imitation Game - Updated Edition, Princeton University Press; Princeton, 2014, Revised Edition.
21. Isaacson, Eugene, and Keller, Herbert B.; Analysis of Numerical Methods, over Publications, New York, 1994; originally published by John Wiley & Sons, Inc., New York, 1966.
22. Johansson, Robert; Numerical Python: A Practical Techniques Approach for Industry, Apress, New York, 2015.
23. Kahaner, David, Moler, Cleve, and Nash, Stephen; Numerical Methods and Software, Prentice-Hall, Englewood Cliffs, NJ, 1989.
24. Maron, Melvin J., and Lopez, Robert J.; Numerical Analysis, a Practical Approach, Wadsworth, Belmont, CA, 1991 (3rd edition).
25. Muller, Jean-Michel, et al.; Handbook of Floating-Point Arithmetic (Second Edition), Birkhauser, 2018.
26. O’Regan, Gerard; A Brief History of Computing, Springer-Verlag, London, 2008.
27. Roulstone, Ian, and Norbury, John, Invisible in the Storm-The Role of Mathematics in Understanding Weather, Princeton University Press, Princeton, NJ, 2013.
28. Shetterly, Margot Lee; Hidden Figures: The American Dream and the Untold Story of the Black Women Mathematicians Who Helped Win the Space Race, William Morrow, New York, 2016.
29. Stoer, J., and Bulirsch, R.; Introduction to Numerical Analysis, Springer-Verlag, New York, 1980.
30. Alefeld, G. E., Potra, F. A., and Shi, Y., “Enclosing zeroes of continuous functions, " ACM Trans. Math. Software, vol. 21, no. 3, pp. 327-344, 1995.
31. Atkinson, Kendall, An Introduction to Numerical Analysis, JohnWiley & Sons, Inc., New York, 1989 (2nd edition).
32. Boyd, John P., “Finding the zeros of a univariate equation: proxy rootfinders, Chebyshev interpolation, and the companion matrix, " SIAM Review, vol. 55, no. 2, pp. 375-396, 2013.
33. Boyd, John P., Solving Transcendental Equations: The Chebyshev Polynomial Proxy and Other Numerical Rootfinders, Perturbation Series, and Oracles, SIAM, 2014.
34. Boyer, Carl, A History of Mathematics, JohnWiley & Sons, Inc., New York, (1st edition), 1968.
35. Brent, Richard, Algorithms for Minimization Without Derivatives, Prentice-Hall, Englewood Cliffs, NJ, 1973.
36. Chun, Changbum, and Neta, Beny, “A new sixth-order scheme for nonlinear equations, " Appl. Math. Lett., vol. 25, pp. 185-189, 2012.
37. Dekker, T., “Finding a zero by means of successive linear interpolation, " in Constructive Aspects of the Fundamental Theorem of Algebra, Dejon, and Henrici, eds., John Wiley & Sons, Inc. New York, 1969.
38. Durand, Emile, Solutions numeriques des equations algebriques. Tome I: Equations du type F(x) = 0; racines d’un polynome, (French) Masson et Cle, Editeurs, Paris, 1960.
39. Goldstine, Herman, A History of Numerical Analysis from the 16th Through the 19th Century, Springer-Verlag, New York, 1977.
40. Gutiérrez, J. M., and Hernández, M. A., “An acceleration of Newton’s method: super-Halley method, " Appl. Math. Comput., vol. 117, pp. 223-239, 2001.
41. Hahn, Alexander J., Basic Calculus: From Archimedes to Newton to its Role in Science, Springer-Verlag, New York, 1998.
42. Hirst, Holly P., and Macey, Wade T., “Bounding the roots of polynomials, " The College Mathematics Journal, vol. 28, no. 4, pp. 292-295, 1997.
43. Householder, Alston, The Numerical Treatment of a Single Nonlinear Equation, McGraw-Hill, New York, 1970.
44. Jenkins, M., and Traub, J., “A three-stage variable shift algorithm for polynomial zeros and its relation to generalized Rayleigh iteration, " Numer. Math., vol. 14, pp. 252-263, 1970.
45. Kerner, Immo O., “Ein Gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen, " Numer. Math., vol. 8, pp. 290-294, 1966.
46. Nedzhibov, Gyurhan H., “Convergence of the modified inverse Weierstrass method for simultaneous approximation of polynomial zeros, " Comm. Num. Anal., vol. 1, pp. 74-80, 2016.
47. Neta, Beny, Scott, Melvin, and Chun, Changbum, “Basins of attraction for several methods to find simple roots of nonlinear equations, " Appl. Math. Comput., vol. 218, pp. 10548-10566, 2012.
48. Ostrowski, Alexander, Solution of Equations and Systems of Equations, Academic Press, New York, 1966.
49. Proinov, Petko D., and Petkova, Milana D., “Convergence of the two-point Weierstrass rootfinding method, " Japan J. Indust. Appl. Math., vol. 31, pp. 279-292, 2014.
50. Proinov, Petko D., and Petkova, Milana D., “A new semilocal convergence theorem for the Weierstrass method for finding zeros of a polynomial simultaneously, " J. Complexity, vol. 30, pp. 366-380, 2014.
51. Traub, Joseph, Iterative Methods for the Solution of Equations, Prentice-Hall, Englewood Cliffs, NJ, 1964.
52. Wait, R. A., The Numerical Solution of Algebraic Equations, JohnWiley&Sons, Inc., Chichester, UK, 1979.
53. Ahlberg, J. H., Nilson, E. N., and Walsh, J. L., The Theory of Splines and Their Applications, Academic Press, New York, 1967.
54. Akima, Hiroshi, “A new method of interpolation and smooth curve fitting based on local procedures, " J. ACM, vol. 17, no. 4, pp. 589-602, 1970.
55. Akima, Hiroshi, “A method of bivariate interpolation and smooth surface fitting based on local procedures, " Comm. ACM, vol. 17 no. 1, pp. 18-20, 1974.
56. Birkhoff, Garrett; “Fluid dynamics, reactor computations, and surface representation, " in A History of Scientific Computation (Steve Nash, editor), 1990.
57. Boyd, John P., Chebyshev and Fourier Spectral Methods, Dover Press, Mineola, New York, 2001.
58. Cheney, E.W., Approximation Theory, Chelsea, New York, 1966.
59. Cline, A. K. “Scalar- and planar-valued curve fitting using splines under tension, " Commun. ACM vol. 17, pp. 218-220 (1974).
60. Davis, Paul; “B-splines and geometric design, " SIAM News, vol. 29, no. 5, 1996.
61. Davis, Philip, Interpolation and Approximation, Dover, New York, 1975; originally published by Blaisdell Publishing Company (1963).
62. de Boor, Carl, “On uniform approximation by splines, " J. Approx. Theory, vol. 1, pp. 219-235, 1968.
63. de Boor, Carl, A Practical Guide to Splines, Springer-Verlag, New York, 1978.
64. Epperson, James, “On the Runge example, " Am. Math. Monthly, vol. 94, no. 4, pp. 329-341, 1987.
65. Fox, L. and Parker, I. B., Chebyshev Polynomials in Numerical Analysis, Oxford University Press, London, 1968.
66. Fritsch, F. N. and Carlson, R. E., “Monotone piecewise cubic interpolation, " SIAM J. Num. Anal., vol. 17, pp.238-246, 1988.
67. Hall, C. A., “On error bounds for spline interpolation, " J. Approx. Theory, vol. 1, pp. 209-218, 1968.
68. Isaacson, E., and Keller, H. B., Analysis of Numerical Methods, over, New York, 1994; originally published by John Wiley & Sons, Inc., 1966.
69. Marusic, Miljenko, and Rogina, Mladen, “B-spline in tension, " VII Conference on Applied Mathematics, Univ. Osijek, Osijek, Yugoslavia, pp. 129-134, 1990.
70. Powell, M. J. D., Approximation Theory and Methods, Cambridge University Press, Cambridge, UK, 1981.
71. Rivlin, Theodore J., An Introduction to the Approximation of Functions, Dover, New York, 1981; originally published by Blaisdell Publishing Company (1969).
72. Schoenberg, I. J., “Contributions to the problem of approximation of equidistant data by analytic functions, " Quart. Appl. Math., vol. 4, pp. 45-99 and 112-141, 1946.
73. Schweikert, D. G., “An interpolating curve using a spline in tension, " J. Math. Phys., vol. 45, pp. 312-317, 1966.
74. Trefethen, L. N., Approximation Theory and Approximation Practice, SIAM, Philadelphia, 2012.
75. Young, David, “Garrett Birkhoff and applied mathematics, " Notices AMS, vol. 44, no. 11, pp. 1446-1449, 1997.
76. Abramowitz, M., and Stegun, I. A., Handbook of Mathematical Functions, Government Printing Office, Washington, DC, 1964. This is a classic resource, and an updated online version exists at http://dlmf.nist.gov/.
77. Atkinson, Kendall, An Introduction to Numerical Analysis, JohnWiley & Sons, Inc., New York, 1989, 2nd edition.
78. Davis, P., and Rabinowitz, P., Methods of Numerical Integration, Academic Press, New York, 1984, 2nd edition.
79. de Doncker, E., and Piessens, R., “Algorithm 32: Automatic computation of integrals with singular integrand, over a finite or infinite range, " Computing, vol. 17, pp. 265-279, 1976.
80. Dutka, Jacques, “Richardson extrapolation and Romberg integration, " Hist. Math., vol. 11, pp. 3-21
81. Gander, W. and Gautschi, W.; “Adaptive quadrature revisited, " BIT, Vol. 40, pp. 84-101, 2000.
82. Gonnet, P., “Increasing the reliability of adaptive quadrature using explicit interpolants, " ACM Trans. Math. Software, vol. 37, no. 3, 2010.
83. Mathias, Roy, “A derivation of Gaussian integration, " Int. J. Math. Educ. Sci. Tech., vol. 28, pp. 134-137 (1997).
84. Piessens, R., et al, QUADPACK: A subroutine package for automatic integration, SpringerVerlag, New York, 1983.
85. Robbins, Herbert, “A remark on Stirling’s formula, " Amer. Math. Monthly, vol. 62, no. 1, pp. 26-29, 1955.
86. Shampine, L.F., “Vectorized adaptive quadrature inMATLAB, " J. Comp. Appl. Math., vol. 211, pp.131-140, 2008.
87. Villarino, Mark B., “Gauss on Gaussian quadrature, " Amer. Math. Monthly, vol. 127, no. 2, pp. 125-138, 2020.
88. Allen, Myron B., and Isaacson, Eli L.; Numerical Analysis for Applied Science, John Wiley & Sons, Inc., New York, 1998.
89. Atkinson, Kendall, An Introduction to Numerical Analysis, JohnWiley & Sons, Inc., New York, 1987 (2nd edition).
90. Bogacki, P., and Shampine, L. F., “A 3(2) pair of Runge-Kutta formulas, " Appl. Math. Lett., vol. 2, pp. 1-9, 1989.
91. Bogucz, E. A., and Walker, J. D. A., “Fourth-order finite difference methods for two-point boundary-value problems, " IMA J. Num. Anal., vol. 4, pp. 69-82, 1984.
92. Bracken, J., “Lanchester models of the Ardennes Campaign, " Naval Research Logistics, vol. 42, no.4, 1995.
93. Braun, Martin, Differential Equations and Their Applications, Springer-Verlag, New York, 1993 (4th Edition).
94. Brauer, Fred, and Castillo-Chavez, Carlos, Mathematical Models for Communicable Diseases, SIAM, Philadelphia, 2013.
95. Burden, Richard, and Faires, J. Douglas, Numerical Analysis, Brooks/Cole, Pacific Grove, CA, 1997 (6th Edition).
96. Chawla, M. M. and Shivakumar, P. N., “An efficient finite difference method for two-point boundary problems, " Neural, Parallel, & Scientific Computations, vol. 4 (1996), pp. 387-396.
97. Chawla, M. M., “Afourth-order tridiagonal finite difference method for general two-point boundary value problems with nonlinear boundary conditions, " J. Inst. Maths Applics., vol. 22 (1978), pp. 89-97.
98. Chawla, M. M., “A sixth-order tridiagonal finite difference method for general nonlinear twopoint boundary value problems, " J. Inst. Maths Applics., vol. 24 (1979), pp. 35-42, 1979.
99. Collatz, L., The Numerical Treatment of Differential Equations, Springer-Verlag, New York, 1966.
100. Coddington, E. A., and Levinson, N., Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.
101. Dormand, J. R., and Prince, P. J., “A family of embedded Runga-Kutta formulae, " J. Comp. Appl. Math., vol. 6, no. 1, pp. 19-26, 1980.
102. Eriksson, K., Estep, D., Hansbo, P., and Johnson, C., Computational Differential Equations, Cambridge University Press, Cambridge, UK, 1996.
103. Gear, C.William, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1971.
104. Goldstine, Herman H., A History of Numerical Analysis from the 16th Through the 19th Century, Springer-Verlag, New York, 1977.
105. Henrici, Peter; Discrete Variable Methods in Ordinary Differential Equations, John Wiley & Sons, Inc., New York, 1962.
106. Isaacson, E., and Keller, H. B., Analysis of Numerical Methods, Dover, New York, 1994; originally published by John Wiley & Sons, Inc., New York, 1966.
107. Iserles, Arieh, A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, Cambridge, UK, 1996.
108. Keller, H. B., Numerical Solution of Two Point Boundary Value Problems, SIAM, Philadelphia, 1976.
109. Kermack, W. O. and McKendrick, A. G., “A contribution to the mathematical theory of epidemics, " Proc. Roy. Soc. London, vol. 115, pp. 700721, London, 1927.
110. Lambert, J. D., Computational Methods for Ordinary Differential Equations, John Wiley & Sons, Inc., London, 1973.
111. Lanchester, F.W., Aircraft in warfare, the dawn of the fourth arm, London, Constable and Company Limited, 1916.
112. Noumerov, B. N., “A method of Extrapolation of Perturbations, " Monthly Notices of the Royal Astronomical Society, Vol. 84, p.592-592, 1924.
113. Shampine, L. F., and Gordon, M. K., Computer Solution of Ordinary Differential Equations, W.H. Freeman and Company, San Francisco, 1975.
114. Shampine, L. F., “The MATLAB ODE Suite, " SIAM J. Sci. Comput., vol. 18, pp. 1-22, 1997.
115. Shampine, L. F., “Vectorized Solution of ODEs in MATLAB, " available online at http://faculty.smu.edu/shampine/current.html.
116. Shampine, L. F., “Vectorized Solution of ODEs in MATLAB with Control of Residual and Error, " available online at http://faculty.smu.edu/shampine/current.html.
117. Weiss, Herbert K., “Combat Models and Historical Data: The U.S. Civil War, " Operations Research, vol. 14, no. 5, pp. 759-790, 1966.
118. Datta, Biswa Nath, Numerical Linear Algebra and Applications, Brooks/Cole, Pacific Grove, CA, 1995.
119. Demmel, James, Applied Numerical Linear Algebra, SIAM, Philadelphia, 1997.
120. Forsythe, George, and Moler, Cleve, Computer Solution of Linear Algebraic Systems, PrenticeHall, Englewood Cliffs, NJ, 1967.
121. Golub, G., and van Loan, C., Matrix Computations, Johns Hopkins Press, Baltimore, 2012 (Fourth edition).
122. Householder, Alston, The Theory of Matrices in Numerical Analysis, Dover, 1975 (originally published by Blaisdell Publishing Co., 1964).
123. Kelley, C. T., Iterative Methods for Linear and Nonlinear Equations, SIAM, Philadelphia, 1995.
124. Ortega, J. M., and Rheinboldt, W. C., Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
125. Saad, Yousef, Iterative Methods for Sparse Linear Systems, PWS Publishing, Boston, 1996.
126. Stewart, G. W., Introduction to Matrix Computations, Academic Press, Orlando, FL, 1973.
127. Trefethen, L. N., and Bau, David, Numerical Linear Algebra, SIAM, Philadelphia, 1997.
128. Watkins, David, Fundamentals of Matrix Computations, John Wiley & Sons, Inc., New York (3rd Edition), 2010.
129. Wilkinson, J. H., Rounding Errors in Algebraic Processes, PrenticeHall, Englewood Cliffs, NJ, 1963.
130. Abramowitz, M., and Stegun, I. A., Handbook of Mathematical Functions, Government Printing Office, Washington, DC, 1964. This is a classic resource, and an updated online version exists at http://dlmf.nist.gov/.
131. Francis, J. G. F., “The QR transformation, part I, " Computer J., vol. 4, pp. 265-272, 1961.
132. Francis, J. G. F., “The QR transformation, part II, " Computer J., vol. 4 pp. 332-345, 1961.
133. Gubner, John A., “Gaussian Quadrature and the Eigenvalue Problem, " unpublished manuscript, https://gubner.ece.wisc.edu/gaussquad.pdf, 2014; accessed 1/28/2020.
134. Golub, Gene; and Uhlig, Frank, “The QR algorithm: 50 years later its genesis by John Francis and Vera Kublanovskaya and subsequent developments, " IMA J. Numer. Anal., vol. 29 (2009), no. 3, 467-485, 2009.
135. Golub, Gene H., and Welsch, John H., “Calculation of Gauss Quadrature Rules, " Math. Comp., Vol. 23, No. 106, pp. 221-230, 1969.
136. Horn, Roger, and Johnson, Charles, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985.
137. Householder, Alston, The Theory of Matrices in Numerical Analysis, Dover, New York, 1975 (originally by Blaisdell Publishing Co., New York, 1964).
138. Parlett, Beresford, The Symmetric Eigenvalue Problem, IAM Classics in Applied Mathematics, SIAM, Philadelphia, 1998; originally published by Prentice-Hall, 1980.
139. Trefethen, L. N., and Bau, David, Numerical Linear Algebra, SIAM, Philadelphia, 1997.
140. Watkins, David, Fundamentals of Matrix Computations, John Wiley & Sons, Inc., New York (3rd Edition), 2010.
141. Watkins, David, “Understanding the QR algorithm, " SIAM Rev., vol. 24, pp. 427-440, 1982.
142. Watkins, David, “Francis’s algorithm, " Amer. Math. Monthly, vol. 118, no. 5, 387-403, 2011.
143. Wilkinson, J. H., The Algebraic Eigenvalue Problem, Oxford University Press, New York, 1965.
144. Ames, W. F., Numerical Methods for Partial Differential Equations, Academic Press, New York, 1977.
145. Birkhoff, Garrett, Numerical Solution of Elliptic Problems, SIAM, Philadelphia, 1971.
146. Briggs, William L., Henson, Van Emden, and McCormick, Steven F., A Multigrid Tutorial (Second Edition), SIAM, Philadelphia, 2000.
147. Birkhoff, Garrett, and Lynch, Robert, Numerical Solution of Elliptic Problems, SIAM, Philadelphia, 1984.
148. Brenner, Suzanne, and Scott, Ridgway, The Mathematical Theory of Finite Element Methods, Springer-Verlag, New York, 1994.
149. Collatz, Lothar, The Numerical Treatment of Differential Equations, Springer-Verlag, Berlin, 1960.
150. Courant, Richard, Friedrichs, Karl, andLewy, Hans, “Uber die partiellenDifferenzengleichungen der mathematischen Physik, " Mathematische Annalen, (in German), vol. 100, no. 1, pp. 32-74, 1928.
151. Datta, Biswa Nath, Numerical Linear Algebra and Applications, Brooks/Cole, Pacific Grove, California, 1995.
152. Duff, Ian, Erisman, A. M., and Reid, J. K., Direct Methods for Sparse Matrices, Oxford University Press, Oxford, UK, 1989.
153. Forsythe, George, and Wasow, Wolfgang, Finite-Difference Methods for Partial Differential Equations, John Wiley & Sons, Inc., New York, 1960.
154. Gupta, Murli, “High Accuracy Compact Difference Schemes for Differential Equations in Mathematical Sciences”, Ann. Math. Sci. Applics., vol. 5, no. 1, pp. 101-138, 2020.
155. Hageman, L. A., and Young, David, Applied Iterative Methods, Academic Press, New York 1981.
156. Humi, Mayer, and Miller, William B., Boundary Value Problems and Partial Differential Equations, PWS-Kent, Boston, 1992.
157. Kelley, C. T., Iterative Methods for Linear and Nonlinear Equations, SIAM, Philadelphia, 1995.
158. LeVeque, Randall, Numerical Methods for Conservation Laws, Birkhauser, Basel, Switzerland, 1990.
159. Morton, K. W., and Mayers, D. F. Numerical Solution of Partial Differential Equations, Cambridge University Press, Cambridge, UK, 1994.
160. Saad, Yousef, Iterative Methods for Sparse Linear Systems, PWS Publishing, Boston, 1996.
161. Smith, G. D., Numerical Solution of Partial Differential Equations: Finite Difference Methods, The Clarendon Press, Oxford University Press, New York, 1985.
162. Strang, Gilbert, and Fix, George; An Analysis of the Finite Element Method, >rentice-Hall, Inc, Englewood Cliffs, NJ 1st Edition, 1973; Wellesley-Cambridge, Cambridge, MA, 2nd Edition, 2008.
163. Strikwerda, John, Finite Difference Schemes and Partial Differential Equations, Wadsworth & Brooks/Cole, Pacific Grove, CA, 1989.
164. Watkins, David, Fundamentals of Matrix Computations, John Wiley & Sons, New York, 3rd Edition, 2010.
165. Young, David, Iterative Solution of Large Linear Systems, Academic Press, New York, 1971.
166. Atkinson, Kendall; An Introduction to Numerical Analysis, JohnWiley & Sons, Inc., New York, 1989 (2nd edition).
167. Boyd, John, “Exponentially convergent Fourier-Chebyshev quadrature schemes on bounded and infinite intervals, " J. Sci. Comput., vol. 2, pp. 99-109, 1987.
168. Boyd, John, Chebyshev and Fourier Spectral Methods, , over, New York, 2001, 2nd Edition; originally published by Springer-Verlag, 1989.
169. Canuto, C., Quarteroni, A., Hussaini, M. Y., and Zang, T. A., Spectral Methods: Fundamentals in Single Domains, Springer-Verlag, Berlin, 2006.
170. Clenshaw, C. W., and Curtis, A. R., “A method for numerical integration on an automatic computer, " Numer. Math., vol. 2, pp. 197-205, 1960.
171. Fornberg, Bengt, A Practical Guide to Pseudospectral Methods, Cambridge University Press, Cambridge, UK, 1995.
172. Fornberg, Bengt, and Flyer, Natasha, A Primer on Radial Basis Functions with Applications to the Geosciences, SIAM, 2015.
173. Gheorghiu, C. I., Spectral Methods for Differential Problems, Casa Cartii de Stiinta, Cluj-Napoca, Romania, 2007. (Out of print, available online at:http://www.ictp.acad.ro/gheorghiu/spectral.pdf.)
174. Golub, G. H., and Welsch, J. H., “Calculation of Gauss quadrature rules, " Math. Comp., vol. 23, pp. 221-230, 1969.
175. Gottleib, David, and Orszag, Steven A., Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, Philadelphia, 1977.
176. Trefethen, L. N., Spectral Methods in MATLAB, SIAM, Philadelphia, 2000.
177. Trefethen, L. N., “Is Gauss quadrature better than Clenshaw-Curtis?" SIAM Rev., vol. 50, no. 1, pp. 67-87, 2008.