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On monotonicity of the Lanczos approximation to the matrix exponential

✍ Scribed by Vladimir Druskin

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 92 KB
Volume: 429
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.04.046

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✦ Synopsis

We prove strictly monotonic error decrease in the Euclidian norm of the Krylov subspace approximation of exp(A)ϕ, where ϕ 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.

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