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Methods for modifying matrix factorizations. (English) Zbl 0289.65021

65F30 Other matrix algorithms (MSC2010)
15A06 Linear equations (linear algebraic aspects)
15A39 Linear inequalities of matrices
90C05 Linear programming
90C20 Quadratic programming
90C30 Nonlinear programming
Full Text: DOI
[1] R. H. Bartels, G. H. Golub, and M. A. Saunders, Numerical techniques in mathematical programming, Nonlinear Programming (Proc. Sympos., Univ. of Wisconsin, Madison, Wis., 1970) Academic Press, New York, 1970, pp. 123 – 176. · Zbl 0228.90030
[2] John M. Bennett, Triangular factors of modified matrices, Numer. Math. 7 (1965), 217 – 221. · Zbl 0132.36204 · doi:10.1007/BF01436076 · doi.org
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[5] \( \ast\) 5. P. E. Gill & W. Murray, A Numerically Stable Form of the Simplex Algorithm, National Physical Laboratory, DNAM Report Number 87, Teddington, England, 1970.
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[7] \( \ast\) 7. P. E. Gill & W. Murray, Two Methods For the Solution of Linearly Constrained and Unconstrained Optimization Problems, National Physical Laboratory, DNAC Report Number 25, Teddington, England, 1972.
[8] G. H. Golub and M. A. Saunders, Linear least squares and quadratic programming, Integer and nonlinear programming, North-Holland, Amsterdam, 1970, pp. 229 – 256. · Zbl 0334.90034
[9] \( \ast\) 9. G. H. Golub & P. H. Styan, Numerical Computations for Univariate Linear Models, Computer Science Department Report Number CS-236-71, Stanford University, Stanford, California, 1971.
[10] Richard J. Hanson and Charles L. Lawson, Extensions and applications of the Householder algorithm for solving linear least squares problems, Math. Comp. 23 (1969), 787 – 812. · Zbl 0185.40701
[11] R. S. Martin, G. Peters & J. H. Wilkinson, ”The QR algorithm for real Hessenberg matrices,” Handbook for Automatic Computation, Vol. 2. Edited by J. H. Wilkinson and C. Reinsch, Springer-Verlag, Berlin and New York, 1971, pp. 359-371. · Zbl 0194.46901
[12] \( \ast\) 12. W. Murray, An Algorithm for Indefinite Quadratic Programming, National Physical Laboratory, DNAC Report Number 1, Teddington, England, 1971.
[13] G. Peters & J. H. Wilkinson, ”The least squares problem and pseudo-inverses,” Comput. J., v. 13, 1970, pp. 309-316. · Zbl 0195.44804
[14] \( \ast\) 14. M. A. Saunders, Large-Scale Linear Programming Using the Cholesky Factorization, Computer Science Department Report Number CS-72-252, Stanford University, Stanford, California, 1972.
[15] \( \ast\) 15. M. A. Saunders, Product Form of the Cholesky Factorization for Large-Scale Linear Programming, Computer Science Department Report Number CS-72-301, Stanford University, Stanford, Calif., 1972.
[16] J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. · Zbl 0258.65037
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