Evaluating non-analytic functions of matrices

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:462

Article

Sharon, Nir¹  Shkolnisky, Yoel² 

[1] Princeton Univ, Program Appl & Computat Math, Princeton, NJ 08544 USA

[2] Tel Aviv Univ, Sch Math Sci, Tel Aviv, Israel

关键词: Matrix functions;    Chebyshev polynomials;    Matrix Chebyshev expansion;    Convergence rates;    Jordan blocks;   

DOI  :  10.1016/j.jmaa.2018.02.029

来源: Elsevier

【 摘 要 】

The paper revisits the classical problem of evaluating f (A) for a real function f and a matrix A with real spectrum. The evaluation is based on expanding f in Chebyshev polynomials, and the focus of the paper is to study the convergence rates of these expansions. In particular, we derive bounds on the convergence rates which reveal the relation between the smoothness of f and the diagonalizability of the matrix A. We present several numerical examples to illustrate our analysis. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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