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Deuflhard, P.; Sautter, W.

On rank-deficient pseudoinverses. (English) Zbl 0452.65019

Linear Algebra Appl. 29, 91-111 (1980).
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Cited in 6 Documents

MSC:

65F20 Numerical solutions to overdetermined systems, pseudoinverses
65F35 Numerical computation of matrix norms, conditioning, scaling

Keywords:

rank-deficient pseudoinverses; Householder triangularization; QRQ- decomposition; error analysis; comparison

Citations:

Zbl 0185.407; Zbl 0195.448
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Full Text: DOI

References:

[1] Businger, P.; Golub, G. H., Linear least squares solutions by Householder transformations, Numer. Math., 7, 269-276 (1965) · Zbl 0142.11503
[2] Deuflhard, P., Ein Newton-Verfahren bei fastsingulärer Funktionalmatrix zur Lösung von nichtlinearen Randwertaufgaben mit der Mehrzielmethode, (Dissertation (1972), Universität Köln, Mathematisches Institut)
[3] Deuflhard, P., A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting, Numer. Math., 22, 289-315 (1974) · Zbl 0313.65070
[4] Deuflhard, P., A stepsize control for continuation methods and its application to multiple shooting techniques, Numer. Math., 33, 115-146 (1979) · Zbl 0428.65032
[5] Golub, G. H.; Reinsch, C., Singular value decomposition and least squares solutions, Numer. Math., 14, 403-420 (1970) · Zbl 0181.17602
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[7] Hanson, R. J.; Lawson, C. L., Extensions and applications of the Householder algorithm for solving linear least squares problems, Math. Comp., 23, 787-812 (1969) · Zbl 0185.40701
[8] Householder, A. S., Unitary triangularization of a nonsymmetric matrix, J. Assoc. Comput. Mach., 5, 339-342 (1958) · Zbl 0121.33802
[9] Householder, A. S., The Theory of Matrices in Numerical Analysis (1964), Blaisdell: Blaisdell New York · Zbl 0161.12101
[10] Levenberg, K. A., A method for the solution of certain nonlinear problems in least squares, Quart. Appl. Math., 2, 164-168 (1944) · Zbl 0063.03501
[11] Marquardt, D. W., An algorithm for least-squares-estimation of nonlinear parameters, SIAM J. Appl. Math., 11, 431-441 (1963) · Zbl 0112.10505
[12] Moore, E. H., On the reciprocal of the general algebraic matrix, Bull. Amer. Math. Soc., 26, 394-395 (1919/20), Abstract
[13] Penrose, R., A generalized inverse for matrices, Proc. Cambridge Philos. Soc., 51, 406-413 (1955) · Zbl 0065.24603
[14] Peters, G.; Wilkinson, J. H., The least squares problem and pseudoinverses, Comput. J., 13, 309-316 (1970) · Zbl 0195.44804
[15] Rutishauser, H., Once again: the least squares problem, Linear Algebra and Appl., 1, 479-488 (1968) · Zbl 0169.19502
[16] Sautter, W., Fehleranalyse für die Gauss-Elimination zur Berechnung der Lösung minimaler Länge, Numer. Math., 30, 165-184 (1978) · Zbl 0425.65024
[17] Stewart, G. W., On the continuity of the generalized inverse, SIAM J. Appl. Math., 17, 33-45 (1969) · Zbl 0172.03801
[18] Varah, J. M., On the numerical solution of ill-conditioned linear systems with applications to ill-posed problems, SIAM J. Numer. Anal., 10, 257-267 (1973) · Zbl 0261.65034
[19] Wilkinson, J. H., The Algebraic Eigenvalue Problem (1965), Clarendon: Clarendon Oxford · Zbl 0258.65037
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