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Mathematics of Computation

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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: 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] 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)
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  • [4] J. H. Wilkinson, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965. MR 32 #1894. MR 0184422 (32:1894)

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Keywords: Error analysis, linear equations, mathematical programming
Article copyright: © Copyright 1973 American Mathematical Society

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