An error analysis of a method for solving matrix equations
Author:
C. C. Paige
Journal:
Math. Comp. 27 (1973), 355359
MSC:
Primary 65F05
MathSciNet review:
0331745
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Abstract: Let be a decomposition of the m by n matrix B of rank m such that L is lower triangular and Q is orthonormal. It is possible to solve , using L but not Q, in the following manner: solve , solve , and form . It is shown that the numerical stability of this method is comparable to that of the method which uses Q. This is important for some methods used in mathematical programming where B is very large and sparse and Q is discarded to save storage.
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Peter
Businger and Gene
H. Golub, Handbook series linear algebra. Linear least squares
solutions by Householder transformations, Numer. Math.
7 (1965), 269–276. MR 0176590
(31 #862)
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P. E. Gill & W. Murray, A Numerically Stable Form of the Simplex Algorithm, Maths. Report No. 87, National Physical Laboratory, Teddington, England, August 1970.
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M. A. Saunders, LargeScale Linear Programming Using the Cholesky Factorization, Computer Science Department Report No. CS 252, Stanford University, Stanford, Calif., January 1972.
 [4]
J.
H. Wilkinson, The algebraic eigenvalue problem, Clarendon
Press, Oxford, 1965. MR 0184422
(32 #1894)
 [1]
 P. Businger & G. H. Golub, "Handbook series linear algebra. Linear least squares solutions by Householder transformations," Numer. Math., v. 7, 1965, pp. 269276. MR 31 #862. MR 0176590 (31:862)
 [2]
 P. E. Gill & W. Murray, A Numerically Stable Form of the Simplex Algorithm, Maths. Report No. 87, National Physical Laboratory, Teddington, England, August 1970.
 [3]
 M. A. Saunders, LargeScale Linear Programming Using the Cholesky Factorization, Computer Science Department Report No. CS 252, Stanford University, Stanford, Calif., January 1972.
 [4]
 J. H. Wilkinson, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965. MR 32 #1894. MR 0184422 (32:1894)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197303317451
PII:
S 00255718(1973)03317451
Keywords:
Error analysis,
linear equations,
mathematical programming
Article copyright:
© Copyright 1973 American Mathematical Society
