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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0053}, url = {http://global-sci.org/intro/article_detail/cicp/12763.html} }