Fast verified computation for the matrix principal pth root

摘要

A fast iterative algorithm for numerically computing an interval matrix containing the principal pth root of an n×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(n3+pn) operations per iteration. The algorithm moreover verifies the uniqueness of the contained pth root. Numerical results show the efficiency of the algorithm.