zbMATH — the first resource for mathematics

A direct method for the solution of sparse linear least squares problems. (English) Zbl 0471.65021

65F20 Numerical solutions to overdetermined systems, pseudoinverses
65D10 Numerical smoothing, curve fitting
90C05 Linear programming
65K05 Numerical mathematical programming methods
Full Text: DOI
[1] Barrodale, I.; Stuart, G., A new variant of Gaussian elimination, J. inst. math. appl., 19, 39-47, (1977) · Zbl 0344.65009
[2] Bauer, F.L., Optimal scaling of matrices and the importance of the minimal condition, (), 198-201 · Zbl 0135.37501
[3] Björck, Å., Methods for sparse linear least squares problems, (), 177-199 · Zbl 0734.65031
[4] Björck, Å., Numerical algorithms for linear least squares problems, () · Zbl 0734.65031
[5] Buzbee, B.L.; Dorr, F.W.; George, J.A.; Golub, G.H., The direct solution of the discrete Poisson equation on irregular regions, SIAM J. numer. anal., 8, 722-736, (1971) · Zbl 0231.65083
[6] Duff, I.S., \scma28—a set of \scfortran subroutines for sparse unsymmetric linear equations, Harwell report AERE-R 8730, (1977)
[7] Duff, I.S.; Reid, J.K., A comparison of some methods for the solution of sparse overdetermined systems of linear equations, J. inst. math. appl., 17, 267-280, (1976) · Zbl 0329.65026
[8] Erisman, A.M.; Tinney, W.F., On computing certain elements of the inverse of a sparse matrix, Comm. ACM, 18, 177-179, (1975) · Zbl 0296.65012
[9] Farebrother, R.W., An historical note on the least squares updating formulas, () · Zbl 0715.65027
[10] George, A.; Heath, M.T., Solution of sparse linear least squares problems using givens rotations, Linear algebra and appl., 34, 69-83, (1980) · Zbl 0459.65025
[11] Haskell, K.H.; Hanson, R.J., An algorithm for linear least squares problems with equality and nonnegativity constraints, () · Zbl 0461.90056
[12] Lawson, C.L.; Hanson, R.J., Solving least squares problems, (1974), Prentice-Hall · Zbl 0185.40701
[13] Markowitz, H.M., The elimination form of the inverse and its application to linear programming, Management sci., 3, 255-269, (1957) · Zbl 0995.90592
[14] Peters, G.; Wilkinson, J.H., The least squares problem and pseudoinverses, Comput. J., 13, 309-316, (1970) · Zbl 0195.44804
[15] Powell, M.J.D.; Reid, J.K., On applying Householder transformations to linear least squares problems, (), 122-126 · Zbl 0194.47002
[16] Reid, J.K., A note on the stability of Gaussian elimination, J. inst. math. appl., 8, 374-375, (1971) · Zbl 0229.65030
[17] Saunders, M., Sparse least squares by conjugate gradients: a comparison of preconditioning methods, Proceedings of computer science and statistics, 12th annual symposium on the interface, (1979)
[18] van der Sluis, A., Condition numbers and equilibration of matrices, Numer. math., 14, 14-23, (1969) · Zbl 0182.48906
[19] Stewart, G.W., Research, development and \sclinpack, (), 1-14
[20] Wilkinson, J.H., The algebraic eigenvalue problem, (1965), Oxford U.P · Zbl 0258.65037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.