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

MSC:
 65F20 Numerical solutions to overdetermined systems, pseudoinverses 65D10 Numerical smoothing, curve fitting 90C05 Linear programming 65K05 Numerical mathematical programming methods
MA28
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References:
 [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
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