TY - JOUR T1 - A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices JO - Communications in Computational Physics VL - 2 SP - 564 EP - 585 PY - 2018 DA - 2018/10 SN - 25 DO - http://doi.org/10.4208/cicp.OA-2018-0053 UR - https://global-sci.org/intro/article_detail/cicp/12763.html KW - Matrix $p$-th root, iteration function, order of convergence, symmetric positive definite matrices, Newton-Schulz, Altman hyperpower method. AB -

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.