{"page":"564-585","doi":"10.4208/cicp.OA-2018-0053","issue":"2","date_created":"2017-07-25T14:48:26Z","abstract":[{"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.","lang":"eng"}],"quality_controlled":"1","project":[{"_id":"32","grant_number":"PL 595/2-1 / 320898746","name":"Performance and Efficiency in HPC with Custom Computing"},{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"publication":"Communications in Computational Physics","type":"journal_article","date_updated":"2023-09-26T11:45:02Z","language":[{"iso":"eng"}],"citation":{"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={<a href=\"https://doi.org/10.4208/cicp.OA-2018-0053\">10.4208/cicp.OA-2018-0053</a>}, 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} }","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. <i>Communications in Computational Physics</i>. 2019;25(2):564-585. doi:<a href=\"https://doi.org/10.4208/cicp.OA-2018-0053\">10.4208/cicp.OA-2018-0053</a>","mla":"Richters, Dorothee, et al. “A General Algorithm to Calculate the Inverse Principal P-Th Root of Symmetric Positive Definite Matrices.” <i>Communications in Computational Physics</i>, vol. 25, no. 2, Global Science Press, 2019, pp. 564–85, doi:<a href=\"https://doi.org/10.4208/cicp.OA-2018-0053\">10.4208/cicp.OA-2018-0053</a>.","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,” <i>Communications in Computational Physics</i>, vol. 25, no. 2, pp. 564–585, 2019, doi: <a href=\"https://doi.org/10.4208/cicp.OA-2018-0053\">10.4208/cicp.OA-2018-0053</a>.","short":"D. Richters, M. Lass, A. Walther, C. Plessl, T. Kühne, Communications in Computational Physics 25 (2019) 564–585.","apa":"Richters, D., Lass, M., Walther, A., Plessl, C., &#38; Kühne, T. (2019). A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices. <i>Communications in Computational Physics</i>, <i>25</i>(2), 564–585. <a href=\"https://doi.org/10.4208/cicp.OA-2018-0053\">https://doi.org/10.4208/cicp.OA-2018-0053</a>","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.” <i>Communications in Computational Physics</i> 25, no. 2 (2019): 564–85. <a href=\"https://doi.org/10.4208/cicp.OA-2018-0053\">https://doi.org/10.4208/cicp.OA-2018-0053</a>."},"user_id":"15278","external_id":{"arxiv":["1703.02456"]},"volume":25,"department":[{"_id":"27"},{"_id":"518"},{"_id":"304"},{"_id":"104"}],"_id":"21","title":"A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices","author":[{"full_name":"Richters, Dorothee","last_name":"Richters","first_name":"Dorothee"},{"last_name":"Lass","id":"24135","full_name":"Lass, Michael","orcid":"0000-0002-5708-7632","first_name":"Michael"},{"full_name":"Walther, Andrea","last_name":"Walther","first_name":"Andrea"},{"first_name":"Christian","orcid":"0000-0001-5728-9982","full_name":"Plessl, Christian","last_name":"Plessl","id":"16153"},{"first_name":"Thomas","full_name":"Kühne, Thomas","last_name":"Kühne","id":"49079"}],"publisher":"Global Science Press","year":"2019","intvolume":"        25","status":"public"}