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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

An error analysis of a method for solving matrix equations


Author: C. C. Paige
Journal: Math. Comp. 27 (1973), 355-359
MSC: Primary 65F05
MathSciNet review: 0331745
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ B = [L\;0]Q$ 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 $ Bx = b$, using L but not Q, in the following manner: solve $ Ly = b$, solve $ {L^T}w = y$, and form $ x = {B^T}w$. 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.


References [Enhancements On Off] (What's this?)

  • [1] 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)
  • [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 0184422 (32 #1894)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1973-0331745-1
PII: S 0025-5718(1973)0331745-1
Keywords: Error analysis, linear equations, mathematical programming
Article copyright: © Copyright 1973 American Mathematical Society