Volume 25, Issue 2
A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices

Dorothee Richters ,  Michael Lass ,  Andrea Walther ,  Christian Plessl and Thomas D. Kühne

10.4208/cicp.OA-2018-0053

Commun. Comput. Phys., 25 (2019), pp. 564-585.

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  • Abstract

We address the general mathematical problem of computing the inverse p-th root of a given matrix in an efficient way. A new method to construct iteration functions that allow calculating arbitrary p-th roots and their inverses of symmetric positive definite matrices is presented. We show that the order of convergence is at least quadratic and that adjusting a parameter q leads to an even faster convergence. In this way, a better performance than with previously known iteration schemes is achieved. The efficiency of the iterative functions is demonstrated for various matrices with different densities, condition numbers and spectral radii.

  • History

Published online: 2018-10

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