An error analysis of a method for solving matrix equations

Author:
C. C. Paige

Journal:
Math. Comp. **27** (1973), 355-359

MSC:
Primary 65F05

DOI:
https://doi.org/10.1090/S0025-5718-1973-0331745-1

MathSciNet review:
0331745

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Abstract | References | Similar Articles | Additional Information

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.

**[1]**P. Businger & G. H. Golub, "Handbook series linear algebra. Linear least squares solutions by Householder transformations,"*Numer. Math.*, v. 7, 1965, pp. 269-276. 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,*Large-Scale 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:
https://doi.org/10.1090/S0025-5718-1973-0331745-1

Keywords:
Error analysis,
linear equations,
mathematical programming

Article copyright:
© Copyright 1973
American Mathematical Society