Error Formulas for Block Rational Krylov Approximations of Matrix Functions

IF 3.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2026-08-20 DOI:10.1137/25m1751815

Stefano Massei, Leonardo Robol

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 64, Issue 4, Page 1733-1763, August 2026.
Abstract. This paper investigates explicit expressions for the error associated with the block rational Krylov approximation of matrix functions. Two formulas are proposed, both derived from characterizations of the residual of the block full orthogonal method. The first formula employs a block generalization of the residual polynomial, while the second leverages the block collinearity of the residuals. A posteriori error bounds based on the knowledge of spectral information of the argument are derived and tested on a set of examples. Notably, both error formulas and their corresponding upper bounds do not require the use of quadratures for their practical evaluation.

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矩阵函数块有理Krylov近似的误差公式

SIAM数值分析杂志，64卷，第4期，第1733-1763页，2026年8月。摘要。本文研究了矩阵函数块有理克雷洛夫近似误差的显式表达式。提出了两个公式，都是由块全正交法的残差特征推导出来的。第一个公式采用残差多项式的块泛化，而第二个公式利用残差的块共线性。基于参数谱信息的知识推导了后验误差界，并在一组实例上进行了测试。值得注意的是，这两个误差公式及其相应的上界在实际计算中都不需要使用正交法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.