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Given an $n$ by $n$ matrix $A$ and an $n$-vector $b$, along with a rational function $R(z) := D(z )^{-1} N(z)$, we show how to find the optimal approximation to $R(A) b$ from the Krylov space, $\mbox{span}( b, Ab, \ldots , A^{k-1} b)$, using the basi
Externí odkaz:
http://arxiv.org/abs/2306.17308
Autor:
Greenbaum, Anne, Wellen, Natalie
We use results in [M. Crouzeix and A. Greenbaum,Spectral sets: numerical range and beyond, SIAM Jour. Matrix Anal. Appl., 40 (2019), pp. 1087-1101] to derive a variety of K-spectral sets and show how they can be used in some applications. We compare
Externí odkaz:
http://arxiv.org/abs/2302.05535
Autor:
Greenbaum, Anne, Wellen, Natalie
Publikováno v:
In Linear Algebra and Its Applications 1 August 2024 694:52-77