A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices
Richters, Dorothee
Lass, Michael
Walther, Andrea
Plessl, Christian
Kühne, Thomas
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.
Global Science Press
2018
info:eu-repo/semantics/article
doc-type:article
text
https://ris.uni-paderborn.de/publication/21
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. <i>Communications in Computational Physics</i>. 2018.
eng
info:eu-repo/semantics/altIdentifier/arxiv/1703.02456
info:eu-repo/grantAgreement/EC/PL 595/2-1
info:eu-repo/semantics/closedAccess