Sensitivity analysis of the Lanczos reduction

Paige, CC;Van Dooren, Paul
(1999) Czech/US Workshop on Interative Methods and Parallel Computing — Location: MILOVY(Czech Republic) (16.June.1997)

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  • Paige, CC
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  • Van Dooren, PaulUCLouvain
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Abstract
For a given real n x 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. Copyright (C) 1999 John Wiley & Sons, Ltd.
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Paige, C., & Van Dooren, P. (1999). Sensitivity analysis of the Lanczos reduction. Numerical Linear Algebra with Applications, 6(1), 29-50. https://doi.org/10.1002/(SICI)1099-1506(199901/02)6:1<29::AID-NLA144>3.0.CO;2-I (Original work published 1999)