10.4208/cicp.OA-2018-0053
Richters, Dorothee
Dorothee
Richters
Lass, Michael
Michael
Lass0000-0002-5708-7632
Walther, Andrea
Andrea
Walther
Plessl, Christian
Christian
Plessl0000-0001-5728-9982
Kühne, Thomas
Thomas
Kühne
A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices
Global Science Press
2019
2017-07-25T14:48:26Z
2019-01-03T13:12:46Z
journal_article
https://ris.uni-paderborn.de/record/21
https://ris.uni-paderborn.de/record/21.json
1703.02456
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 adaptively adjusting a parameter q
always 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.