---
_id: '21'
abstract:
- lang: eng
text: "We address the general mathematical problem of computing the inverse p-th\r\nroot
of a given matrix in an efficient way. A new method to construct iteration\r\nfunctions
that allow calculating arbitrary p-th roots and their inverses of\r\nsymmetric
positive definite matrices is presented. We show that the order of\r\nconvergence
is at least quadratic and that adaptively adjusting a parameter q\r\nalways leads
to an even faster convergence. In this way, a better performance\r\nthan with
previously known iteration schemes is achieved. The efficiency of the\r\niterative
functions is demonstrated for various matrices with different\r\ndensities, condition
numbers and spectral radii."
author:
- first_name: Dorothee
full_name: Richters, Dorothee
last_name: Richters
- first_name: Michael
full_name: Lass, Michael
id: '24135'
last_name: Lass
orcid: 0000-0002-5708-7632
- first_name: Andrea
full_name: Walther, Andrea
last_name: Walther
- first_name: Christian
full_name: Plessl, Christian
id: '16153'
last_name: Plessl
orcid: 0000-0001-5728-9982
- first_name: Thomas
full_name: Kühne, Thomas
id: '49079'
last_name: Kühne
citation:
ama: Richters D, Lass M, Walther A, Plessl C, Kühne T. A General Algorithm to Calculate
the Inverse Principal p-th Root of Symmetric Positive Definite Matrices. *Communications
in Computational Physics*. 2019;25(2):564-585. doi:10.4208/cicp.OA-2018-0053
apa: Richters, D., Lass, M., Walther, A., Plessl, C., & Kühne, T. (2019). A
General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive
Definite Matrices. *Communications in Computational Physics*, *25*(2),
564–585. https://doi.org/10.4208/cicp.OA-2018-0053
bibtex: '@article{Richters_Lass_Walther_Plessl_Kühne_2019, title={A General Algorithm
to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices},
volume={25}, DOI={10.4208/cicp.OA-2018-0053},
number={2}, journal={Communications in Computational Physics}, publisher={Global
Science Press}, author={Richters, Dorothee and Lass, Michael and Walther, Andrea
and Plessl, Christian and Kühne, Thomas}, year={2019}, pages={564–585} }'
chicago: 'Richters, Dorothee, Michael Lass, Andrea Walther, Christian Plessl, and
Thomas Kühne. “A General Algorithm to Calculate the Inverse Principal P-Th Root
of Symmetric Positive Definite Matrices.” *Communications in Computational Physics*
25, no. 2 (2019): 564–85. https://doi.org/10.4208/cicp.OA-2018-0053.'
ieee: D. Richters, M. Lass, A. Walther, C. Plessl, and T. Kühne, “A General Algorithm
to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices,”
*Communications in Computational Physics*, vol. 25, no. 2, pp. 564–585, 2019.
mla: Richters, Dorothee, et al. “A General Algorithm to Calculate the Inverse Principal
P-Th Root of Symmetric Positive Definite Matrices.” *Communications in Computational
Physics*, vol. 25, no. 2, Global Science Press, 2019, pp. 564–85, doi:10.4208/cicp.OA-2018-0053.
short: D. Richters, M. Lass, A. Walther, C. Plessl, T. Kühne, Communications in
Computational Physics 25 (2019) 564–585.
date_created: 2017-07-25T14:48:26Z
date_updated: 2019-01-03T13:12:46Z
department:
- _id: '27'
- _id: '518'
- _id: '304'
- _id: '104'
doi: 10.4208/cicp.OA-2018-0053
external_id:
arxiv:
- '1703.02456'
intvolume: ' 25'
issue: '2'
language:
- iso: eng
page: 564-585
project:
- _id: '32'
grant_number: PL 595/2-1
name: Performance and Efficiency in HPC with Custom Computing
publication: Communications in Computational Physics
publisher: Global Science Press
status: public
title: A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric
Positive Definite Matrices
type: journal_article
user_id: '24135'
volume: 25
year: '2019'
...