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Methods for modifying matrix factorizations. (English) Zbl 0289.65021

MSC:
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
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[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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