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"citation" : {
"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. https://doi.org/10.4208/cicp.OA-2018-0053.",
"short" : "D. Richters, M. Lass, A. Walther, C. Plessl, T. Kühne, Communications in Computational Physics 25 (2019) 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. *Communications in Computational Physics*. 2019;25(2):564-585. doi:10.4208/cicp.OA-2018-0053",
"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*, vol. 25, no. 2, Global Science Press, 2019, pp. 564–85, doi:10.4208/cicp.OA-2018-0053.",
"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.",
"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. https://doi.org/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} }"
},
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"doi" : "10.4208/cicp.OA-2018-0053",
"language" : [
{
"iso" : "eng"
}
],
"author" : [
{
"last_name" : "Richters",
"first_name" : "Dorothee",
"full_name" : "Richters, Dorothee"
},
{
"first_name" : "Michael",
"full_name" : "Lass, Michael",
"id" : "24135",
"last_name" : "Lass",
"orcid" : "0000-0002-5708-7632"
},
{
"last_name" : "Walther",
"full_name" : "Walther, Andrea",
"first_name" : "Andrea"
},
{
"first_name" : "Christian",
"full_name" : "Plessl, Christian",
"id" : "16153",
"last_name" : "Plessl",
"orcid" : "0000-0001-5728-9982"
},
{
"full_name" : "Kühne, Thomas",
"first_name" : "Thomas",
"last_name" : "Kühne",
"id" : "49079"
}
],
"_version" : 13,
"intvolume" : " 25",
"page" : "564-585",
"date_created" : "2017-07-25T14:48:26Z",
"publisher" : "Global Science Press",
"external_id" : {
"arxiv" : [
"1703.02456"
]
},
"creator" : {
"id" : "24135",
"login" : "lass"
},
"volume" : 25,
"status" : "public",
"year" : "2019",
"project" : [
{
"grant_number" : "PL 595/2-1",
"_id" : "32",
"name" : "Performance and Efficiency in HPC with Custom Computing"
}
],
"publication" : "Communications in Computational Physics",
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"issue" : "2",
"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"
}
],
"date_updated" : "2019-01-03T13:12:46Z",
"title" : "A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices"
}]