[{"author":[{"last_name":"Richters","first_name":"Dorothee"},{"last_name":"Lass","first_name":"Michael","orcid":"0000-0002-5708-7632","id":"24135"},{"first_name":"Andrea","last_name":"Walther"},{"last_name":"Plessl","first_name":"Christian","orcid":"0000-0001-5728-9982","id":"16153"},{"first_name":"Thomas","last_name":"Kühne","id":"49079"}],"external_id":{"arxiv":[]},"creator":{"login":"lass","id":"24135"},"date_updated":"2018-08-06T09:28:26Z","uri_base":"https://ris.uni-paderborn.de","publication":"Communications in Computational Physics","_id":"21","_version":10,"dini_type":"doc-type:article","type":"journal_article","dc":{"rights":["info:eu-repo/semantics/closedAccess"],"creator":["Richters, Dorothee","Lass, Michael","Walther, Andrea","Plessl, Christian","Kühne, Thomas"],"relation":["info:eu-repo/semantics/altIdentifier/arxiv/1703.02456","info:eu-repo/grantAgreement/EC/PL 595/2-1"],"title":["A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices"],"identifier":["https://ris.uni-paderborn.de/publication/21"],"language":["eng"],"source":["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*. 2018."],"type":["info:eu-repo/semantics/article","doc-type:article","text"],"date":["2018"],"description":["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."],"publisher":["Global Science Press"]},"department":[{"tree":[{"_id":"216"},{"_id":"43"}],"_id":"27"},{"tree":[{"_id":"7"},{"_id":"34"},{"_id":"44"},{"_id":"43"}],"_id":"518"},{"tree":[{"_id":"165"},{"_id":"2"},{"_id":"35"},{"_id":"44"},{"_id":"43"}],"_id":"304"},{"_id":"104","tree":[{"_id":"99"},{"_id":"10"},{"_id":"34"},{"_id":"44"},{"_id":"43"}]}],"language":[{}],"date_created":"2017-07-25T14:48:26Z","project":[{"_id":"32","name":"Performance and Efficiency in HPC with Custom Computing"}],"citation":{"short":"D. Richters, M. Lass, A. Walther, C. Plessl, T. Kühne, Communications in Computational Physics (2018).","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*, 2018.","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* (2018): n. pag. Print.","apa":"Richters, D., Lass, M., Walther, A., Plessl, C., & Kühne, T. (2018). A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices. *Communications in Computational Physics*.","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*, 2018.","bibtex":"@article{Richters_Lass_Walther_Plessl_Kühne_2018, title={A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices}, 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={2018}}"},"status":"public","file":[],"abstract":[{"lang":"eng"}],"user_id":"24135"}]