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