[{"user_id":"24135","publisher":"Global Science Press","publication":"Communications in Computational Physics","issue":"2","date_created":"2017-07-25T14:48:26Z","language":[{"iso":"eng"}],"_id":"21","author":[{"full_name":"Richters, Dorothee","last_name":"Richters","first_name":"Dorothee"},{"last_name":"Lass","orcid":"0000-0002-5708-7632","first_name":"Michael","id":"24135","full_name":"Lass, Michael"},{"first_name":"Andrea","last_name":"Walther","full_name":"Walther, Andrea"},{"orcid":"0000-0001-5728-9982","first_name":"Christian","last_name":"Plessl","id":"16153","full_name":"Plessl, Christian"},{"id":"49079","full_name":"Kühne, Thomas","last_name":"Kühne","first_name":"Thomas"}],"department":[{"tree":[{"_id":"216"},{"_id":"43"}],"_id":"27"},{"tree":[{"_id":"7"},{"_id":"34"},{"_id":"44"},{"_id":"43"}],"_id":"518"},{"_id":"304","tree":[{"_id":"613"},{"_id":"2"},{"_id":"35"},{"_id":"44"},{"_id":"43"}]},{"tree":[{"_id":"99"},{"_id":"10"},{"_id":"34"},{"_id":"44"},{"_id":"43"}],"_id":"104"}],"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.","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}}","short":"D. Richters, M. Lass, A. Walther, C. Plessl, T. Kühne, Communications in Computational Physics 25 (2019) 564.","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* 25.2 (2019): 564–585. Web.","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. 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. http://doi.org/10.4208/cicp.OA-2018-0053"},"year":"2019","date_updated":"2018-10-25T14:02:55Z","volume":25,"intvolume":" 25","page":"564-585","external_id":{"arxiv":["1703.02456"]},"project":[{"_id":"32","name":"Performance and Efficiency in HPC with Custom Computing","grant_number":"PL 595/2-1"}],"type":"journal_article","doi":"10.4208/cicp.OA-2018-0053","title":"A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices","_version":12,"creator":{"id":"24135","login":"lass"},"status":"public","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."}]}]