Least squares methods

Handbook of Numerical Analysis

Volumn 1, Issue , 1990, Pages 465-652

  Björck, Åke ^a  

^a LINKÖPING UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70350657102     PISSN: 15708659     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1570-8659(05)80036-5     Document Type: Review

References (287)

1. Abdelmalek N.N. Roundoff error analysis for Gram-Schmidt method and solution of linear least squares problems. BIT 11 (1971) 345-368
2. Al-Baali M., and Fletcher R. An efficient line search for nonlinear least-squares. J. Optim. Theory Appl. 48 (1986) 359-377
3. Anderson N., and Karasalo I. On computing bounds for the least singular value of a triangular matrix. BIT 15 (1975) 1-4
4. Ashkenazi V. Geodetic normal equations. In: Reid J.K. (Ed). Large Sets of Linear Equations (1971), Academic Press, Moscow 57-74
5. Avila J.K., and Tomlin J.A. Solution of very large least squares problems by nested dissection on a parallel processor. Proceedings Computer Science and Statistics: Twelfth Annual Symposium on the Interface. Waterloo, Ont (1979)
6. Bard Y. Nonlinear Parameter Estimation (1974), Academic Press, New York
7. Bareiss E.H. Numerical solution of the weighted linear least squares problems by G-transformations. SIAM J. Algebraic Discrete Methods (1983)
8. Barlow J.L. Stability analysis of the G-algorithm and a note on its application to sparse least squares problems. BIT 25 (1985) 507-520
9. Barrodale I., and Phillips C. Algorithm 495: Solution of an overdetermined system of linear equations in the Chebychev norm. ACM Trans. Math. Software 1 (1975) 264-270
10. 1 linear approximation. SIAM J. Numer. Anal. 10 (1973) 839-848
11. ∞ sense. SIAM J. Numer. Anal. 15 (1978) 255-270
12. 1 solution to an overdetermined linear system. SIAM J. Numer. Anal. 15 (1978) 224-241
13. Bauer F.L. Elimination with weighted row combinations for solving linear equations and least squares problems. Numer. Math 7 (1965) 338-352
14. Berman, and Plemmons R.J. Cones and iterative methods for best least squares solutions of linear systems. SIAM J. Numer. Anal. 11 (1974) 145-154
15. Björck Å. Solving linear least squares problems by Gram-Schmidt orthogonalization. BIT 7 (1967) 1-21
16. Björck Å. Iterative refinement of linear least squares solutions. I. BIT 7 (1967) 257-278
17. Björck Å. Iterative refinement of linear least squares solutions. II. BIT 8 (1968) 8-30
18. Björck Å. Methods for sparse least squares problems. In: Bunch J.R., and Rose D.J. (Eds). Sparse Matrix Computations (1976), Academic Press, New York 177-199
19. Björck Å. Comment on the iterative refinement of least squares solutions. J. Amer. Statist. Assoc. 73 (1978) 161-166
20. Björck Å. SSOR preconditioning methods for sparse least squares problems. Proceedings Computer Science and Statistics: Twelfth Annual Symposium on the Interface. Waterloo, Ont (1979)
21. Björck Å. A general updating algorithm for constrained linear least squares problems. SIAM J. Sci. Statist. Comput. 5 (1984) 394-402
22. Björck Å. Stability analysis of the method of semi-normal equations for least squares problems. Linear Algebra Appl. 88/89 (1987) 31-48
23. Björck Å. A bidiagonalization algorithm for solving ill-posed systems of linear equations. BIT 28 (1988) 659-670
24. Björck Å., and Duff I.S. A direct method for the solution of sparse linear least squares problems. Linear Algebra Appl. 34 (1980) 43-67
25. Björck Å., and Eldén L. Methods in numerical algebra for ill-posed problems. Rept. LiTH-MAT-R-33-79 (1979), Linköping University, New York
26. Björck Å., and Elfving T. Accelerated projection methods for computing pseudoinverse solutions of systems of linear equations. BIT 19 (1979) 145-163
27. Björck Å., and Golub G.H. Iterative refinement of linear least square solutions by Householder transformation. BIT 7 (1967) 322-337
28. Björck Å., and Golub G.H. Numerical methods for computing angles between linear subspaces. Math. Comp. 27 (1973) 579-594
29. Björck Å., Plemmons R.J., and Schneider H. Large-Scale Matrix Problems (1981), North-Holland, Linköping, Sweden
30. Boggs P.T., Byrd R.H., and Schnabel R.B. A stable and efficient algorithm for nonlinear orthogonal regression. SIAM J. Sci. Statist. Comput. 8 (1987) 1052-1078
31. Bojanczyk A., and Brent R.P. Parallel solution of certain Toeplitz least squares problems. Linear Algebra Appl. 77 (1986) 43-60
32. Bojanczyk A., Brent R.P., van Dooren P., and de Hoog F. A note on downdating the Cholesky factorization. SIAM J. Sci. Statist. Comput. 8 (1987) 210-221
33. Bolstad J.H., et al. Numerical analysis program library user's guide. User Note 82 (1978), SLAC Computer Services, Stanford Linear Accelerator Center, New York
34. Bunch J.R., and Kaufman L. Some stable methods for calculating inertia and solving symmetric linear systems. Math. Comp. 31 (1977) 162-179
35. Bunch J.R., Kaufmann L., and Parlett B.N. Decomposition of a symmetric matrix. Numer. Math. 27 (1976) 95-109
36. Bunch J.R., and Nielsen C.P. Updating the singular value decomposition. Numer. Math. 31 (1978) 111-129
37. Bunch J.R., and Parlett B.N. Direct methods for solving symmetric indefinite systems of linear equations. SIAM J. Numer. Anal. 8 (1971) 639-655
38. In: Bunch J.R., and Rose D.J. (Eds). Sparse Matrix Computations (1976), Academic Press, Menlo Park, CA
39. Businger P., and Golub G.H. Linear least squares solutions by Householder transformations. Numer. Math. 7 (1965) 269-276
40. Businger P.A., and Golub G.H. Algorithm 358: Singular value decomposition of a complex matrix. Comm. ACM 12 (1969) 564-565
41. Chan T.F. An improved algorithm for computing the singular value decomposition. ACM Trans. Math. Software 8 (1982) 72-83
42. Chan T.F. Algorithm 581: An improved algorithm for computing the singular value decomposition. ACM Trans. Math. Software 8 (1982) 84-88
43. Chan T.F. Rank revealing QR-factorizations. Linear Algebra Appl. 88/89 (1987) 67-82
44. Chen Y.T. Iterative methods for linear least squares problems. Rept. CS-75-04 (1975), University of Waterloo, New York
45. Chen Y.T., and Tewarson R.P. On the fill-in when sparse vectors are orthonomalized. Computing 9 (1972) 53-56
46. Cline A.K. An elimination method for the solution of linear least squares problems. SIAM J. Numer. Anal. 10 (1973) 283-289
47. Cline A.K. The transformation of a quadratic programming problem into solvable form. ICASE Rept. 75-14 (1975), NASA, Langley Research Center, Ont.
48. Cline A.K., Conn A.R., and van Loan C. Generalizing the LINPACK condition estimator. In: Hennart J.P. (Ed). Numerical Analysis. Lecture Notes in Mathematics 909 (1982), Springer, Verlag, Hampton, VA
49. Cline A.K., Moler C.B., Stewart G.W., and Wilkinson J.H. An estimate for the condition number of a matrix. SIAM J. Numer. Anal. 16 (1979) 368-375
50. 2-solutions to underdetermined linear systems. SIAM Rev. 18 (1976) 92-106
51. Coleman T.F., Edenbrandt A., and Gilbert J.R. Predicting fill for sparse orthogonal factorization. J. ACM 33 (1986) 517-532
52. Cox M.G. The least squares solution of overdetermined linear equations having band or augmented band structure. IMA J. Numer. Anal. 1 (1981) 3-22
53. Crane R.L., Garbow B.S., Hillstrom K.E., and Minkoff M. LCLSQ: An implementation of an algorithm for linearly constrained linear least squares problems. Rept. ANL-80-116 (1980), Argonne National Laboratory, New York
54. Craven P., and Wahba G. Smoothing noisy data with spline functions. Numer. Math. 31 (1979) 377-403
55. Cryer C. The solution of a quadratic programming problem using systematic overrelaxation. SIAM J. Control 9 (1971) 385-392
56. Cuthill E. Several strategies for reducing the bandwidth of matrices. In: Rose D.J., and Willoughby R.A. (Eds). Sparse Matrices and Their Applications (1972), Plenum Press, Argonne, IL
57. Daniel J., Gragg W.B., Kaufman L., and Stewart G.W. Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization. Math. Comp. 30 (1976) 772-795
58. Delves L.M., and Barrodale I. A fast direct method for the least squares solution of slightly overdetermined sets of linear equations. J. Inst. Math. Appl. 24 (1979) 149-156
59. Demmel J.W. The smallest perturbation of a submatrix which lowers the rank and constrained total least squares. SIAM J. Numer. Anal. 24 (1987) 199-206
60. Dennis J.E. Nonlinear least squares and equations. In: Jacobs D.A.H. (Ed). The State of the Art in Numerical Analysis (1977), Academic Press, New York 269-312
61. Dennis Jr. J.E., Gay D.M., and Welsch R.E. An adaptive nonlinear least-squares algorithm. ACM Trans. Math. Software 7 (1981) 348-368
62. Dennis Jr. J.E., and Schnabel R.B. Numerical Methods for Unconstrained Optimization and Nonlinear Equations (1983), Prentice-Hall, New York
63. Dennis J.E., and Steihaug T. On the successive projection approach to least squares problems. SIAM J. Numer. Anal. 23 (1986) 717-733
64. Deuflhard P., and Apostolescu V. An underrelaxed Gauss-Newton method for equality constrained nonlinear least squares. In: Stoer J. (Ed). Proceedings 8th IFIP Conference on Optimization Techniques. Lecture Notes in Control and Information Science 7 (1978), Springer, Englewood Cliffs, NJ 22-32
65. Deuflhard P., and Apostolescu V. A study of the Gauss-Newton algorithm for the solution of nonlinear least squares problems. In: Frehse J., Pallaschke D., and Trottenberg U. (Eds). Special Topics of Applied Mathematics (1980), North-Holland, Berlin
66. Dongarra J., Bunch J.R., Moler C.B., and Stewart G.W. LINPACK Users Guide (1979), SIAM, Amsterdam
67. Draper N.R., and Smith H. Applied Regression Analysis. 2nd ed. (1981), Wiley, Philadelphia, PA
68. Duff I.S. Pivot selection and row orderings in Givens reduction on sparse matrices. Computing 13 (1974) 239-248
69. Duff I.S., and Reid J.K. A comparison of some methods for the solution of sparse overdetermined systems of linear equations. J. Inst. Math. Appl. 17 (1976) 267-280
70. Duff I.S., and Reid J.K. MA27-A set of Fortran subroutines for solving sparse symmetric sets of linear equations. Rept. R. 10533 (1982), AERE, New York
71. Duff I.S., and Reid J.K. The multifrontal solution of indefinite sparse symmetric linear systems. ACM Trans. Math. Software 9 (1983) 302-325
72. In: Duff I.S., and Stewart G.W. (Eds). Sparse Matrix Proceedings. 1978 (1979), SIAM, Harwell, England
73. Dwyer P.S. The square root method and its use in correlation and regression. J. Amer. Statist. Assoc. 40 (1945) 493-503
74. Eckhard C., and Young G. The approximation of one matrix by another of lower rank. Psychometrica 1 (1936) 211-218
75. Eichhorn E.L., and Lawson C.L. An ALGOL procedure for solution of constrained least squares problems. Computing Memorandum No. 374 (1975), JPL, Philadelphia, PA
76. Eisenstat S.C., Schultz M.H., and Sherman A.H. Algorithms and data structures for sparse symmetric Gaussian elimination. SIAM J. Sci. Statist. Comput. 2 (1981) 225-237
77. p-approximations. BIT 13 (1973) 292-300
78. Eldén L. Algorithms for the regularization of ill-conditioned least squares problems. BIT 17 (1977) 134-145
79. Eldén L. Perturbation theory for the least squares problem with linear equality constraints. SIAM J. Numer. Anal. 17 (1980) 338-350
80. Eldén L. An efficient algorithm for the regularization of ill-conditioned least squares problems with a triangular Toeplitz matrix. SIAM J. Sci. Statist. Comput. 5 (1984) 229-236
81. Eldén L. An algorithm for the regularization of ill-conditioned banded least squares problems. SIAM J. Sci. Statist. Comput. 5 (1984) 237-254
82. Eldén L. A note on the computation of the generalized cross-validation function for ill-conditioned least squares problems. BIT 24 (1984) 467-472
83. Elfving T. Some numerical results obtained with two gradient methods for solving the linear least squares problem. Rept. LiTH-MAT-R-75-5 (1978), Department of Mathematics, Linköping University, Pasadena, CA
84. Elfving T. Block-iterative methods for consistent and inconsistent linear equations. Numer. Math. 35 (1980) 1-12
85. Erisman A.M., and Tinney W.F. On computing certain elements of the inverse of a sparse matrix. Comm. ACM 18 (1975) 177-179
86. Faddeev D.K., Kublanovskaya V.N., and Faddeeva V.N. Solution of linear algebraic systems with rectangular matrices. Proc. Steklov Inst. Math. 96 (1968)
87. Farebrother R.W. The statistical estimation of the standard linear model, 1756-1853. Proceedings First Tampere Seminar on Linear Models. 1983 (1985) 77-99
88. Fletcher R. Practical Methods of Optimization, 1: Unconstrained Optimization (1980), Wiley, Sweden
89. Fletcher R. Practical Methods of Optimization, 2: Constrained Optimization (1981), Wiley, New York
90. Forsythe G.E., Malcolm M.A., and Moler C. Computer Methods for Mathematical Computations (1977), Prentice-Hall, New York
91. Forsythe G.E., and Moler C. Computer Solution of Linear Algebraic Systems (1967), Prentice-Hall, Englewood Cliffs, NJ
92. Foster L.V. Rank and nullspace calculations using matrix decompositions without column interchanges. Linear Algebra Appl. 74 (1986) 47-71
93. Gander W. Algorithms for the QR-decomposition. Rept. 80-02 Angewandte Mathematik (1980), ETH, Englewood Cliffs, NJ
94. Gander W. Least squares with a quadratic constraint. Numer. Math. 36 (1981) 291-307
95. Gauss C.F. Theoria combinationis observationum erroribus minimis obnoxiae. Commentationes Societas Regiae Scientarium Gottengensis Recentiores 5 (1823) 33-90
96. Gay D.M. Algorithm 611, Subroutines for unconstrained minimization using a model/trust-region approach. ACM Trans. Math. Software 9 (1983) 503-524
97. Gay D.M. A trust-region approach to linearly constrained optimization. In: Griffiths D.F. (Ed). Proceedings 1983 Dundee Conference on Numerical Analysis. Lecture Notes in Mathematics 1066 (1984), Springer, Zürich 72-105
98. Gentleman W.M. Least squares computations by Givens transformations without square roots. J. Inst. Math. Appl. 12 (1973) 329-336
99. Gentleman W.M. Error analysis of QR decompositions by Givens transformations. Linear Algebra Appl. 10 (1975) 189-197
100. Gentleman W.M. Row elimination for solving sparse linear systems and least squares problems. In: Watson G.A. (Ed). Proceedings 1975 Dundee Conference on Numerical Analysis. Lecture Notes in Mathematics 506 (1976), Springer, Berlin 122-133
101. George J.A., and Heath M.T. Solution of sparse linear least squares problems using Givens rotations. Linear Algebra Appl. 34 (1980) 69-73
102. George J.A., Heath M.T., and Ng E.G.Y. A comparison of some methods for solving sparse linear least squares problems. SIAM J. Sci. Statist. Comput. 4 (1983) 177-187
103. George J.A., Heath M.T., and Plemmons R.J. Solution of large-scale least squares problems using auxiliary storage. SIAM J. Sci. Statist. Comput. 2 (1981) 416-429
104. George J.A., and Liu J.W.H. Computer Solution of Large Sparse Positive Definite Systems (1981), Prentice-Hall, Berlin
105. George J.A., Liu J.W.H., and Ng E.G.Y. Row ordering schemes for sparse Givens transformations, I. Bipartite graph model. Linear Algebra Appl. 81 (1984) 55-81
106. George J.A., and Ng E.G.Y. On row and column orderings for sparse least squares problems. SIAM J. Numer. Anal. 20 (1983) 326-344
107. George J.A., and Ng E.G.Y. SPARSPAK: Waterloo sparse matrix package user's guide for SPARSPAK-B. Research Rept. CS-84-37 (1984), Department of Computer Science, University of Waterloo, Englewood Cliffs, NJ
108. George J.A., Poole W.G., and Voigt R.G. Incomplete nested dissection for solving n by n grid problems. SIAM J. Numer. Anal. 15 (1978) 90-112
109. Gill P.E., Golub G.H., Murray W., and Saunders M.A. Methods for modifying matrix factorizations. Math. Comp. 28 (1974) 505-535
110. Gill P.E., Hammarling S.J., Murray W., Saunders M.A., and Wright M.H. User's guide for LSSOL (version 1.0): A Fortran package for constrained linear least-squares and convex quadratic programming. Rept. SOL (1986), Department of Operations Research, Stanford University, Ont.
111. Gill P.E., and Murray W. Nonlinear least squares and nonlinearly constrained optimization. In: Watson G.A. (Ed). Proceedings 1975 Dundee Conference on Numerical Analysis. Lecture Notes in Mathematics 506 (1976), Springer, CA
112. Gill P.E., and Murray W. The orthogonal factorization of a large sparse matrix. In: Bunch J.R., and Rose D.J. (Eds). Sparse Matrix Computations (1976), Academic Press, Berlin 201-212
113. Gill P.E., and Murray W. Algorithms for the solution of the nonlinear least squares problem. SIAM J. Numer. Anal. 15 (1978) 977-992
114. Gill P.E., Murray W., and Wright M.H. Practical Optimization (1981), Academic Press, New York
115. Givens W. Computation of plane unitary rotations transforming a general matrix to triangular form. SIAM J. Appl. Math. 6 (1958) 26-50
116. Golub G.H. Numerical methods for solving linear least squares problems. Numer. Math. 7 (1965) 206-216
117. Golub G.H. Least squares, singular values and matrix approximations. Apl. Mat. 13 (1968) 44-51
118. Golub G.H. Matrix decompositions and statistical computation. In: Milton R.C., and Nelder J.A. (Eds). Statistical Computation (1969), Academic Press, New York 365-397
119. Golub G.H. Some modified matrix eigenvalue problems. SIAM Rev. 15 (1973) 318-344
120. Golub G.H., Heath M.T., and Wahba G. Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21 (1979) 215-223
121. Golub G.H., Hoffman A., and Stewart G.W. A generalization of the Eckhard-Young-Mirsky matrix approximation theorem. Linear Algebra Appl. 88/89 (1987) 317-327
122. Golub G.H., and Kahan W. Calculating the singular values and pseudo-inverse of a matrix. SIAM J. Numer. Anal. Ser. B 2 (1965) 205-224
123. Golub G.H., Klema V., and Stewart G.W. Rank degeneracy and least squares problems. Tech. Rept. TR-456 (1976), Department of Computer Science, University of Maryland, New York
124. Golub G.H., and LeVeque R. Extensions and uses of the variable projection algorithm for solving nonlinear least squares problems. Proceedings of the 1979 Army Numerical Analysis and Computers Conference. ARO Rept. 79-3 (1979)
125. Golub G.H., Luk F.T., and Overton M.L. A block Lanczos method for computing the singular values and corresponding singular vectors of a matrix. ACM Trans. Math. Software 7 (1981) 149-169
126. Golub G.H., Luk F.T., and Pagano M. A sparse least squares problem in photogrammetry. Proceedings Computer Science and Statistics: Twelfth Annual Conference on the Interface. Waterloo, Ont. (1979)
127. Golub G.H., Manneback P., and Toint P. A comparison between some direct and iterative methods for large scale geodetic least squares problems. SIAM J. Sci. Statist. Comput. 7 (1986) 799-816
128. Golub G.H., and Pereyra V. The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. SIAM J. Numer. Anal. 10 (1973) 413-432
129. Golub G.H., and Pereyra V. Differentiation of pseudo-inverses, separable nonlinear least squares problems and other tales. In: Nashed M.Z. (Ed). Generalized Inverses and Applications (1976), Academic Press, College Park, MD 303-324
130. Golub G.H., and Plemmons R.J. Large scale geodetic least squares adjustment by dissection and orthogonal decomposition. Linear Algebra Appl. 34 (1980) 3-27
131. to appear. Golub G.H., Plemmons R.J., and Sameh A. Parallel block schemes for large scale least squares computations (1986)
132. Golub G.H., and Reinsch C. Singular value decomposition and least squares solutions. Numer. Math. 14 (1970) 403-420
133. Golub G.H., and Styan G.P. Numerical computations for univariate linear models. J. Statist. Comput. Simulation 2 (1973) 253-274
134. Golub G.H., and van Loan C.F. An analysis of the total least squares problem. SIAM J. Numer. Anal. 17 (1980) 883-893
135. Golub G.H., and van Loan C.F. Matrix Computations (1983), Johns Hopkins Press, New York
136. Golub G.H., and Varga R.S. Chebyshev semi-iterative methods, successive overrelaxation iterative methods and second order Richardson iterative methods, Parts I and II. Numer. Math. 3 (1961) 147-168
137. Golub G.H., and Wilkinson J.H. Note on the iterative refinement of least squares solutions. Numer. Math. 9 (1966) 139-148
138. Grimes R.G., and Lewis J.G. Condition number estimation for sparse matrices. SIAM J. Sci. Statist. Comput. 2 (1981) 384-388
139. Gustavsson F.G. Finding the block lower triangular form of a matrix. In: Bunch J.R., and Rose D.J. (Eds). Sparse Matrix Computations (1976), Academic Press, Baltimore, MD 275-289
140. Hageman L.A., Luk F.T., and Young D.M. On the equivalence of certain iterative acceleration methods. SIAM J. Numer. Anal. 17 (1980) 852-873
141. Hammarling S. A note on modifications to the Givens plane rotation. J. Inst. Math. Appl. 13 (1974) 215-218
142. Hanson R.J. Linear least squares with bounds and linear constraints. SIAM J. Sci. Statist. Comput. 7 (1986) 826-834
143. Hanson R.J., and Phillips J.L. An adaptive numerical method for solving linear Fredholm equations of the first kind. Numer. Math. 24 (1975) 291-307
144. Haskell K.H., and Hanson R.J. Selected algorithms for the linearly constrained least squares problem: A user's guide. Tech. Rept. SAND78 1290 (1979), Sandia National Laboratories, New York
145. Haskell K.H., and Hanson R.J. An algorithm for linear least squares problems with equality and nonnegativity constraints. Math. Programming 21 (1981) 98-118
146. Heath M.T. Some extensions of an algorithm for sparse linear least squares problems. SIAM J. Sci. Statist. Comput. 3 (1982) 223-237
147. Heath M.T. Numerical methods for large sparse linear least squares problems. SIAM J. Sci. Statist. Comput. 26 (1984) 497-513
148. Helmert F.R. Die mathematischen und physikalischen Theorien der höheren Geodäsie 1 (1880), Teubner, Albuquerque, NM
149. Hestenes M.R., and Stiefel E. Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Standards 49 (1952) 409-436
150. Hiebert K.L. An evaluation of mathematical software that solves nonlinear least squares problems. ACM Trans. Math. Software 7 (1981) 1-16
151. Holt J.N., and Fletcher R. An algorithm for constrained non-linear least-squares. J. Inst. Math. Appl. 23 (1979) 449-463
152. Householder A.S. Unitary triangularization of a nonsymmetric matrix. J. ACM 5 (1958) 339-342
153. Householder A.S. The Theory of Matrices in Numerical Analysis (1974), Dover, Leipzig
154. Huber P.J. Robust Statistical Procedures. CBMS-NSF Regional Conference Series in Applied Mathematics (1977), SIAM, New York
155. Hutchinson M.F., and de Hoog F.R. Smoothing noisy data with spline functions. Numer. Math. 47 (1985) 99-106
156. Jennings L.S., and Osborne M.R. A direct error analysis for least squares. Numer. Math. 22 (1974) 322-332
157. Jordan T.L. Experiments on error growth associated with some linear least-squares procedures. Math. Comp. 22 (1968) 579-588
158. Kahan W. Numerical linear algebra. Canad. Math. Bull. 9 (1966) 757-801
159. Karasalo I. A criterion for truncation of the QR decomposition algorithm for the singular linear least squares problem. BIT 14 (1974) 156-166
160. Kaufman L. Variable projection methods for solving separable nonlinear least squares problems. BIT 15 (1975) 49-57
161. Kaufman L. Application of dense Householder transformation to a sparse matrix. ACM Trans. Math. Software 5 (1979) 442-450
162. Kaufman L., and Pereyra V. A method for separable nonlinear least squares problems with separable nonlinear equality constraints. SIAM J. Numer. Anal. 15 (1978) 12-20
163. Keller J. On the solution of singular and semidefinite linear systems by iterations. J. SIAM Ser. B 2 (1965) 281-290
164. Kolata G.B. Geodesy: dealing with an enormous computer task. Science 200 (1978) 421-422
165. Krogh F.T. Efficient implementation of a variable projection algorithm for nonlinear least squares. Comm. ACM 17 (1974) 167-169
166. Lawson C.L., and Hanson R.J. Extensions and applications of the Householder algorithm for solving linear least squares problems. Math. Comp. 23 (1969) 787-812
167. Lawson C.L., and Hanson R.J. Solving Least Squares Problems (1974), Prentice-Hall, Philadelphia, PA
168. Lawson C.L., Hanson R.J., Krogh F.T., and Kincaid D. Basic linear algebra subprograms for FORTRAN usage. ACM Trans. Math. Software 5 (1979) 308-323
169. Rept. Leringe Ö., and Wedin P.-A. A comparison between different methods to compute a vector x which minimizes ∥Ax-b∥, when Gx=h (1970), Department of Computer Science, Lund University, Englewood Cliffs, NJ
170. Levenberg K. A method for the solution of certain problems in least squares. Quart. Appl. Math. 2 (1944) 164-168
171. Lindström P. A stabilized Gauss-Newton algorithm for unconstrained nonlinear least squares problems. Rept. UMINF-102.82 (1982), Umeå University
172. Lindström P. A general purpose algorithm for nonlinear least squares problems with nonlinear constraints. Rept. UMINF-103.83 (1983), Umeå University, Sweden
173. Lindström P. Two user guides, one (ENLSIP) for constrained-one (ELSUNC) for unconstrained nonlinear least squares problems. Rept. UMINF-109 and 110 (1984), Umeå University, Sweden
174. Lindström P., and Wedin P.-A. A new linesearch algorithm for unconstrained nonlinear least squares problems. Math. Programming. 29 (1984) 268-296
175. Lindström P., and Wedin P.-A. Methods and software for nonlinear least squares problems. Rept. UMINF-133.87 (1986), Umeå University, Sweden
176. Linnik I. Method of Least Squares and Principles of the Theory of Observations (1961), Pergamon Press, Sweden
177. Liu J.W.H. On general row merging schemes for sparse Givens transformations. SIAM J. Sci. Statist. Comput. 7 (1986) 1190-1211
178. Luk F.T. Computing the singular value decomposition on the ILLIAC IV. ACM Trans. Math. Software. 6 (1980) 524-539
179. Läuchli P. Jordan-Elimination und Ausgleichung nach kleinsten Quadraten. Numer. Math. 3 (1961) 226-240
180. Lötstedt P. Solving the minimal least squares problem subject to bounds on the variables. BIT 24 (1984) 206-224
181. Mahdavi-Amiri N. Generally constrained nonlinear least squares and generating test problems: Algorithmic approach. Ph.D. Thesis (1981), Johns Hopkins University, New York
182. Manneback P. On some numerical methods for solving large sparse linear least squares problems. Ph.D. Thesis (1985), Facultés Universitaires Notre-Dame de la Paix, Baltimore, MD
183. Manneback P., Murigande C., and Toint P.L. A modification of an algorithm by Golub and Plemmons for large linear least squares in the context of Doppler positioning. IMA J. Numer. Anal. 5 (1985) 221-234
184. Manteuffel T. An incomplete factorization technique for positive definite linear systems. Math. Comp. 34 (1980) 473-479
185. Markowitz H.M. The elimination form of the inverse and its application to linear programming. Management Sci. 3 (1957) 255-269
186. Marquardt D. An algorithm for least-squares estimation of nonlinear parameters. SIAM J. Appl. Math. 11 (1963) 431-441
187. Mirsky L. Symmetric gauge functions and unitarily invariant norms. Quart. J. Math. Oxford 11 (1960) 50-59
188. Moler C.B. MATLAB user's guide. Tech. Rept. CS81-1 (1980), Department of Computer Science. University of New Mexico, Namur, Belgium
189. Molinari L. Gram-Schmidt'sches Orthogonalisierungsverfahren. In: Gander W., Molinari L., and Svecová H. (Eds). Numerische Prozeduren aus Nachlass und Lehre von Prof. Heinz Rutishauser (1977), Birkhäuser, Albuquerque, NM 77-93
190. Moré J.J. The Levenberg-Marquardt algorithm: Implementation and theory. In: Watson G.A. (Ed). Numerical Analysis, Proceedings Biennial Conference Dundee. Lecture Notes in Mathematics 630 (1978), Springer, Stuttgart 105-116
191. Moré J.J. Recent developments in algorithms and software for trust region-methods. Mathematical Programming: The State of the Art (1983), Springer, Berlin
192. Moré J.J., Garbow B.S., and Hillstrom K.E. User's guide for MINPACK-1. Rept. ANL-80-74 (1980), Applied Mathematics Division, Argonne National Laboratory, Berlin
193. Moré J.J., and Sorenson D.C. Computing a trust region step. SIAM J. Sci. Statist. Comput. 4 (1981) 553-572
194. Nash J.C. A one-sided transformation method for the singular value decomposition and algebraic eigenproblem. Comput. J. 18 (1975) 74-76
195. Nazareth L. Some recent approaches to solving large residual nonlinear least squares problems. SIAM Rev. 22 (1980) 1-11
196. O'Leary D.P. A generalized conjugate gradient algorithm for solving a class of quadratic programming problems. Linear Algebra Appl. 34 (1980) 371-399
197. O'Leary D.P. Estimating matrix condition numbers. SIAM J. Sci. Statist. Comput. 1 (1980) 205-209
198. O'Leary D.P., and Simmons J.A. A bidiagonalization-regularization procedure for large scale discretizations of ill-posed problems. SIAM J. Sci. Statist. Comput. 2 (1981) 474-489
199. Oreborn U. A direct method for sparse nonnegative least squares problems. Lic. Thesis No. 87. Linköping Studies in Science and Technology, 1986 27 (1986), Linköping University, Argonne, IL
200. Ortega J.M., and Rheinboldt W.C. Iterative Solution of Nonlinear Equations in Several Variables (1970), Academic Press, Sweden
201. Osborne E.E. On least squares solutions of linear equations. J. ACM 8 (1961) 628-636
202. Paige C.C. An error analysis of a method for solving matrix equations. Math. Comp. 27 (1973) 355-359
203. Paige C.C. Computer solution and perturbation analysis of generalized least squares problems. Math. Comp. 33 (1979) 171-184
204. Paige C.C. Fast numerically stable computations for generalized linear least squares problems. SIAM J. Numer. Anal. 16 (1979) 165-171
205. Paige C.C. Properties of numerical algorithms related to computing controllability. IEEE Trans. Automat. Control. 26 (1981) 130-138
206. Paige C.C. The general linear model and the generalized singular value decomposition. Linear Algebra Appl. 70 (1985) 269-284
207. Paige C.C. Computing the generalized singular value decomposition. SIAM J. Sci. Statist. Comput. 7 (1986) 1126-1146
208. Paige C.C., and Saunders M.A. Least squares estimation of discrete linear dynamic systems using orthogonal transformations. SIAM J. Numer. Anal. 14 (1977) 180-193
209. Paige C.C., and Saunders M.A. Towards a generalized singular value decomposition. SIAM J. Numer. Anal. 18 (1981) 398-405
210. Paige C.C., and Saunders M.A. LSQR: An algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Software 8 (1982) 43-71
211. Paige C.C., and Saunders M.A. Algorithm 583 LSQR: Sparse linear equations and least squares problems. ACM Trans. Math. Software 8 (1982) 195-209
212. Parlett B.N. Analysis of algorithms for reflections in bisectors. SIAM Rev. 13 (1971) 197-208
213. Parlett B.N. The Symmetric Eigenvalue Problem (1980), Prentice-Hall, New York
214. Parlett B.N., and Reid J.K. On the solution of a system of linear equations whose matrix is symmetric but not definite. BIT 10 (1970) 386-397
215. Patzelt P. Ein Algorithmus zur Lösung von Ausgleichproblemen mit Ungleichungen als Nebenbedingungen. Diplomarbeit (1973), University of Würzburg, Englewood Cliffs, NJ
216. Penrose R. A generalized inverse for matrices. Proc. Cambridge Philos. Soc. 51 (1955) 506-513
217. Peters G., and Wilkinson J.H. The least squares problem and pseudo-inverses. Comput. J. 13 (1970) 309-316
218. Plemmons R.J. Monotonicity and iterative approximations involving rectangular matrices. Math. Comp. 26 (1972) 853-858
219. Plemmons R.J. Linear least squares by elimination and MGS. J. ACM 21 (1974) 581-585
220. Powell M.J.D., and Reid J.K. On applying Householder's method to linear least squares problems. In: Morell A.J.M. (Ed). Proceedings IFIP Congress. 1968 (1969), North-Holland, F.R.G. 122-126
221. Ramsin H., and Wedin P.-A. A comparison of some algorithms for the nonlinear least squares problem. BIT 17 (1977) 72-90
222. Reid J.K. A note on the least squares solution of a band system of linear equations by Householder reductions. Comput. J. 10 (1967) 188-189
223. Reid J.K. On the use of conjugate gradients for systems of linear equations possessing 'Property A". SIAM J. Numer. Anal. 9 (1972) 325-332
224. Reinsch C.H. Smoothing by spline functions. Numer. Math. 16 (1971) 451-454
225. Rice J.R. Experiments on Gram-Schmidt orthogonalization. Math. Comp. 20 (1966) 325-328
226. Rice J.R. PARVEC workshop on very large least squares problems and supercomputers. Rept. CSD-TR 464 (1983), Purdue University, Amsterdam
227. Ruhe A. Accelerated Gauss-Newton algorithms for nonlinear least squares problems. BIT 19 (1979) 356-367
228. Ruhe A. Numerical aspects of Gram-Schmidt orthogonalization of vectors. Linear Algebra Appl. 52/53 (1983) 591-601
229. Ruhe A., and Wedin P.-A. Algorithms for separable nonlinear least squares problems. SIAM Rev. 22 (1980) 318-337
230. Rutishauser H. Description of Algol 60. Handbook of Automatic Computation 1a (1967), Springer, West Lafayette, IN
231. Rutishauser H. Vorlesungen über numerische Mathematik 1 (1976), Birkhäuser, Berlin
232. Saunders M.A. Sparse least squares by conjugate gradients: A comparison of preconditioning methods. Proceedings Computer Science and Statistics: Twelfth Annual Symposium on the Interface. Waterloo, Ont. (1979) 15-20
233. Schittkowski K. The numerical solution of constrained linear least-squares problems. IMA J. Numer. Anal. 3 (1983) 11-36
234. Schittkowski K. Solving constrained nonlinear least squares problems by
235. Schittkowski K., and Stoer J. A factorization method for the solution of constrained linear least squares problems allowing subsequent data changes. Numer. Math. 31 (1979) 431-463
236. Preprint No. 30. Schittkowski K., and Zimmerman P. A factorization method for constrained least squares problems with data changes, Part 2: Numerical tests, comparisons, and ALGOL codes (1977), Institut für Angewandte Mathematik und Statistik, Universität Würzburg, F.R.G.
237. Schwetlick H., and Tiller V. Numerical methods for estimating parameters in nonlinear models with errors in the variables. Technometrics 27 (1985) 17-24
238. Scolnik H.D. On the solution of non-linear least squares problems. In: Freeman H. (Ed). Proceedings IFIP 71 (1972), North-Holland, F.R.G. 1258-1265
239. Seber G.A.F. Linear Regression Analysis (1977), Wiley, Amsterdam
240. Stewart G.W. Introduction to Matrix Computations (1973), Academic Press, New York
241. Stewart G.W. The economical storage of plane rotations. Numer. Math. 25 (1976) 137-138
242. Stewart G.W. On the perturbation of pseudo-inverses, projections, and linear least squares problems. SIAM Rev. 19 (1977) 634-662
243. Stewart G.W. Perturbation bounds for the QR factorization of a matrix. SIAM J. Numer. Anal. 14 (1977) 509-518
244. Stewart G.W. Research, development and LINPACK. In: Rice J.R. (Ed). Mathematical Software II (1977), Academic Press, New York 1-14
245. Stewart G.W. A note on the perturbation of singular values. Linear Algebra Appl. 28 (1979) 213-216
246. Stewart G.W. The effects of rounding error on an algorithm for downdating a Cholesky-factorization. J. Inst. Math. Appl. 23 (1979) 203-213
247. Stewart G.W. The efficient generation of random orthogonal matrices with an application to condition estimators. SIAM J. Numer. Anal. 17 (1980) 403-409
248. Stewart G.W. An algorithm for computing the CS decomposition of a partitioned orthonormal matrix. Numer. Math. 40 (1982) 297-306
249. Stewart G.W. A method for computing the generalized singular value decomposition. In: Kgström B., and Ruhe A. (Eds). Matrix Pencils, Proceedings, Pite Havsbad. 1982. Lecture Notes in Mathematics 973 (1983), Springer, New York 207-220
250. Stewart G.W. Rank degeneracy. SIAM J. Sci. Statist. Comput. 5 (1984) 403-413
251. Stewart G.W. On the invariance of perturbed null vectors under column scaling. Numer. Math. 44 (1984) 61-65
252. Stiefel E. Ausgleichung ohne Aufstellung der Gausschen Normalgleichungen. Wiss. Z. Tech. Hochsch. Dresden 2 (1952/1953) 441-442
253. Stoer J. On the numerical solution of constrained least squares problems. SIAM J. Numer. Anal. 8 (1971) 382-411
254. Tihonov A.N. Regularization of incorrectly posed problems. Dokl. Akad. Nauk SSSR 153 (1963) 1035-1038
255. Toint P.L. On large scale nonlinear least squares calculations. SIAM J. Sci. Statist. Comput. 8 (1987) 416-435
256. van der Sluis A. Condition numbers and equilibration of matrices. Numer. Math. 14 (1969) 14-23
257. van der Sluis A. Stability of the solutions of linear least squares problems. Numer. Math. 23 (1975) 241-254
258. van der Sluis A., and Veltkamp G.W. Restoring rank and consistency by orthogonal projection. Linear Algebra Appl. 28 (1979) 257-278
259. van Loan C. Generalizing the singular value decomposition. SIAM J. Numer. Anal. 13 (1976) 76-83
260. van Loan C. Analysis of some matrix problems using the CS decomposition. Tech. Rept. TR84-603 (1984), Cornell University, Berlin
261. van Loan C. Computing the CS and the generalized singular value decomposition. Rept. TR 84-614 (1984), Cornell University, Ithaca, NY
262. van Loan C. On the method of weighting for equality-constrained least squares problems. SIAM J. Numer. Anal. 22 (1985) 851-864
263. Varah J.M. On the numerical solution of ill-conditioned linear systems with applications to ill-posed problems. SIAM J. Numer. Anal. 10 (1973) 257-267
264. Varah J.M. A lower bound for the smallest singular value of a matrix. Linear Algebra Appl. 11 (1975) 1-2
265. Varah J.M. A practical examination of some numerical methods for linear discrete ill-posed problems. SIAM Rev. 21 (1979) 100-111
266. Varga R.S. Matrix Iterative Analysis (1962), Prentice-Hall, Ithaca, NY
267. Wampler R.H. A report on the accuracy of some widely used least squares computer programs. J. Amer. Statist. Assoc. 65 (1970) 549-565
268. Wampler R.H. Some recent developments in linear least squares computations. In: Tarter M.E. (Ed). Proceedings Computer Science and Statistics: Sixth Annual Symposium on the Interface. Berkeley, CA (1972)
269. Wampler R.H. Solutions to weighted least squares problems by modified Gram-Schmidt with iterative refinement. ACM Trans. Math. Software 5 (1979) 457-465
270. p approximation problems. In: Griffiths D.F. (Ed). Proceedings 1983 Dundee Conference on Numerical Analysis. Lecture Notes in Mathematics 1066 (1984), Springer, Englewood Cliffs, NJ
271. Wedin P.-A. Perturbation bounds in connection with the singular value decomposition. BIT 12 (1972) 99-111
272. Wedin P.-A. On the almost rank-deficient case of the least squares problem. BIT 13 (1973) 344-354
273. Wedin P.-A. Perturbation theory for pseudo-inverses. BIT 13 (1973) 217-232
274. Wedin P.-A. On the Gauss-Newton method for the nonlinear least squares problems. ITM Working Paper 24 (1974), Institutet för Tillämpad Matematik, Berlin
275. Wedin P.-A. Perturbation theory and condition numbers for generalized and constrained linear least squares problems. Rept. UMINF 125.85 (1985), Umeå University, Stockholm
276. Weil R.L., and Kettler P.C. Rearranging matrices to block-angular form for decomposition (and other) algorithms. Management Sci. 18 (1971) 98-108
277. Wilkinson J.H. Rounding Errors in Algebraic Processes (1963), Prentice-Hall, Sweden
278. Wilkinson J.H. The Algebraic Eigenvalue Problem (1965), Clarendon Press, Englewood Cliffs, NJ
279. Wilkinson J.H. A priori error analysis of algebraic processes. Proceedings International Congress on Mathematics (1968), Izdat. Mir, Oxford 629-639
280. Wilkinson J.H. Modern error analysis. SIAM Rev. 13 (1971) 548-568
281. Wilkinson J.H. Some recent advances in numerical linear algebra. In: Jacobs D.A.H. (Ed). The State of the Art in Numerical Analysis (1977), Academic Press, Moscow 1-53
282. In: Wilkinson J.H., and Reinsch C. (Eds). Handbook for Automatic Computation 2, Linear Algebra (1971), Springer, New York
283. Wright S.J., and Holt J.N. Algorithms for nonlinear least squares with linear inequality constraints. SIAM J. Sci. Statist. Comput. 6 (1985) 1033-1048
284. Young D.M. Iterative Solution of Large Systems (1971), Academic Press, New York
285. Zimmermann P. Ein Algorithmus zur Lösung linearer Least Squares Probleme mit unteren und oberen Schranken als Nebenbedingungen, Diplomarbeit (1977), Institut für Angewandte Mathematik und Statistik, Universität Würzburg, New York
286. Zlatev Z. Comparison of two pivotal strategies in sparse plane rotations. Comput. Math. Appl. 8 (1982) 119-135
287. Zlatev Z., and Nielsen H.B. LLSS01: A Fortran subroutine for solving least squares problems (User's guide). Rept. No. 79-07 (1979), Institute of Numerical Analysis, Technical University Denmark, F.R.G.