On the sensitivity of the LU factorization |
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Authors: | Xiao-Wen Chang Christopher C. Paige |
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Affiliation: | (1) Department of Computer Science, University of British Columbia, V6T 1Z4 Vancouver, B.C., Canada;(2) School of Computer Science, McGill University, H3A 2A7 Montreal, Quebec, Canada;(3) Present address: School of Computer Science, McGill University, H3A 2A7 Montreal, Quebec, Canada |
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Abstract: | This paper gives sensitivity analyses by two approaches forL andU in the factorizationA=LU for general perturbations inA which are sufficiently small in norm. By the matrix-vector equation approach, we derive the condition numbers for theL andU factors. By the matrix equation approach we derive corresponding condition estimates. We show how partial pivoting and complete pivoting affect the sensitivity of the LU factorization. The material presented here is a part of the first author's PhD thesis under the supervision of the second author. This research was supported by NSERC of Canada Grant OGP0009236. |
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Keywords: | 15A23 65F35 |
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