期刊
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
卷 40, 期 1, 页码 645-663出版社
SPRINGER JAPAN KK
DOI: 10.1007/s13160-022-00543-w
关键词
Toeplitz matrix inversion; Structured perturbation analysis; Circulant matrix; Invertibility; Fast Fourier transform
This note presents a new structured perturbation analysis method for Toeplitz inversion, which improves the existing upper bounds proposed by Wu et al. and Feng et al. It also provides practical issues and numerical experiments to support the theoretical findings.
The invertibility of a Toeplitz matrix can be assessed based on the solvability of two standard equations. The inverse of the nonsingular Toeplitz matrix can then be represented as the sum of products of circulant and skew-circulant (CS) matrices. In this note, we provide a new structured perturbation analysis for the CS representation of Toeplitz inversion and the new upper bound is just half as large as the existing upper bound proposed by Wu et al. (Numer Linear Algebra Appl 22(4):777-792, 2015) and Feng et al. (East Asian J Appl Math 5(2):160-175, 2015). Meanwhile, some practical issues and numerical experiments involving the numerical solutions of fractional partial differential equations are reported to support our theoretical findings.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据