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Sensitivity analysis of the Lanczos reduction

✍ Scribed by Christopher C. Paige; Paul Van Dooren

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
139 KB
Volume
6
Category
Article
ISSN
1070-5325

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✦ Synopsis

For a given real n Γ— n matrix A and initial vectors v 1 and w 1 , we examine the sensitivity of the tridiagonal matrix T and the biorthogonal sets of vectors of the Lanczos reduction to small changes in A, v 1 and w 1 . We also consider the sensitivity of the developing Krylov subspaces.

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The Unsymmetric Lanczos Reduction (ULR) method is developed to solve the ΓΏnite-element-based solution to the contaminant transport problem. The method sometimes su ers from breakdown when at some step division by a pivot which is zero or near zero, causes numerical instability. In this paper, the Ma