A general algorithm to calculate the inverse principal p-th root of symmetric positive definite matrices
Richters D, Lass M, Walther A, Plessl C, Kühne TD (2019)
Publication Type: Journal article
Publication year: 2019
Journal
Book Volume: 25
Pages Range: 564-585
Journal Issue: 2
DOI: 10.4208/CICP.OA-2018-0053
Abstract
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.
Involved external institutions
Germany (DE)How to cite
APA:
Richters, D., Lass, M., Walther, A., Plessl, C., & Kühne, T.D. (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
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 25.2 (2019): 564-585.
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