[{"external_id":{"arxiv":["1703.02456"]},"author":[{"last_name":"Richters","first_name":"Dorothee","full_name":"Richters, Dorothee"},{"id":"24135","full_name":"Lass, Michael","orcid":"0000-0002-5708-7632","first_name":"Michael","last_name":"Lass"},{"first_name":"Andrea","last_name":"Walther","full_name":"Walther, Andrea"},{"last_name":"Plessl","first_name":"Christian","orcid":"0000-0001-5728-9982","full_name":"Plessl, Christian","id":"16153"},{"full_name":"Kühne, Thomas","id":"49079","last_name":"Kühne","first_name":"Thomas"}],"type":"journal_article","department":[{"_id":"27"},{"_id":"518"},{"_id":"304"},{"_id":"104"}],"date_updated":"2018-08-06T09:28:26Z","_id":"21","publication":"Communications in Computational Physics","publisher":"Global Science Press","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}}","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*. 2018."},"title":"A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices","year":"2018","date_created":"2017-07-25T14:48:26Z","project":[{"name":"Performance and Efficiency in HPC with Custom Computing","grant_number":"PL 595/2-1","_id":"32"}],"language":[{"iso":"eng"}],"user_id":"24135","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."}],"file":[],"status":"public"}]