Faber polynomials of matrices for non-convex sets

Autor:	Beckermann, Bernhard, Crouzeix, Michel
Rok vydání:	2013
Předmět:	Mathematics - Numerical Analysis Mathematics - Classical Analysis and ODEs Mathematics - Functional Analysis
Druh dokumentu:	Working Paper
Popis:	It has been recently shown that $|| F_n(A) ||\leq 2$, where $A$ is a linear continuous operator acting in a Hilbert space, and $F_n$ is the Faber polynomial of degree $n$ corresponding to some convex compact $E\subset \mathbb C$ containing the numerical range of $A$. Such an inequality is useful in numerical linear algebra, it allows for instance to derive error bounds for Krylov subspace methods. In the present paper we extend this result to not necessary convex sets $E$.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1310.1356 Zobrazit plný text záznamu View this record from Arxiv