For a given real n ร 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.
On the sensitivity of Lanczos recursions to the spectrum
โ Scribed by Vladimir Druskin; Liliana Borcea; Leonid Knizhnerman
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 320 KB
- Volume
- 396
- Category
- Article
- ISSN
- 0024-3795
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๐ SIMILAR VOLUMES
We prove strictly monotonic error decrease in the Euclidian norm of the Krylov subspace approximation of exp(A)ฯ, where ฯ and A are respectively a vector and a symmetric matrix. In addition, we show that the norm of the approximate solution grows strictly monotonically with the subspace dimension.
Stability of passing from Gaussian quadrature data to the Lanczos recurrence coefficients is considered. Special attention is paid to estimates explicitly expressed in terms of quadrature data and not having weights in denominators. It has been shown that the recent approach, exploiting integral rep