An error analysis of a method for solving matrix equations
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- by C. C. Paige PDF
- Math. Comp. 27 (1973), 355-359 Request permission
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
- Peter Businger and Gene H. Golub, Handbook series linear algebra. Linear least squares solutions by Householder transformations, Numer. Math. 7 (1965), 269–276. MR 176590, DOI 10.1007/BF01436084 P. E. Gill & W. Murray, A Numerically Stable Form of the Simplex Algorithm, Maths. Report No. 87, National Physical Laboratory, Teddington, England, August 1970. M. A. Saunders, Large-Scale Linear Programming Using the Cholesky Factorization, Computer Science Department Report No. CS 252, Stanford University, Stanford, Calif., January 1972.
- J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Math. Comp. 27 (1973), 355-359
- MSC: Primary 65F05
- DOI: https://doi.org/10.1090/S0025-5718-1973-0331745-1
- MathSciNet review: 0331745