Fast verified computation for the matrix principal pth root

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:330

Article

Miyajima, Shinya¹ 

[1] Iwate Univ, Fac Sci & Engn, Morioka, Iwate 0208551, Japan

关键词: Matrix pth root;    Principal pth root;    Verified computation;   

DOI  :  10.1016/j.cam.2017.08.018

来源: Elsevier

【 摘 要 】

A fast iterative algorithm for numerically computing an interval matrix containing the principal pth root of an n x n matrix A is proposed. This algorithm is based on a numerical spectral decomposition of A, and is applicable when a computed eigenvector matrix of A is not ill-conditioned. Particular emphasis is put on the computational efficiency of the algorithm which has only O(n(3) + pn) operations per iteration. The algorithm moreover verifies the uniqueness of the contained pth root. Numerical results show the efficiency of the algorithm. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free