Parallel approximation of the exponential of Hermitian matrices
In this work, we consider a rational approximation of the exponential function to design an algorithm for computing matrix exponential in the Hermitian case. Using partial fraction decomposition, we obtain a parallelizable method, where the computation reduces to independent resolutions of linear sy...
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| creator | Hecht, Frédéric Kaber, Sidi-Mahmoud Perrin, Lucas Plagne, Alain Salomon, Julien |
| description | In this work, we consider a rational approximation of the exponential
function to design an algorithm for computing matrix exponential in the
Hermitian case. Using partial fraction decomposition, we obtain a
parallelizable method, where the computation reduces to independent resolutions
of linear systems. We analyze the effects of rounding errors on the accuracy of
our algorithm. We complete this work with numerical tests showing the
efficiency of our method and a comparison of its performances with Krylov
algorithms. |
| doi_str_mv | 10.48550/arxiv.2306.16778 |
| format | Article |
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function to design an algorithm for computing matrix exponential in the
Hermitian case. Using partial fraction decomposition, we obtain a
parallelizable method, where the computation reduces to independent resolutions
of linear systems. We analyze the effects of rounding errors on the accuracy of
our algorithm. We complete this work with numerical tests showing the
efficiency of our method and a comparison of its performances with Krylov
algorithms.</description><identifier>DOI: 10.48550/arxiv.2306.16778</identifier><language>eng</language><subject>Computer Science - Distributed, Parallel, and Cluster Computing ; Computer Science - Numerical Analysis ; Mathematics - Numerical Analysis</subject><creationdate>2023-06</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2306.16778$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2306.16778$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Hecht, Frédéric</creatorcontrib><creatorcontrib>Kaber, Sidi-Mahmoud</creatorcontrib><creatorcontrib>Perrin, Lucas</creatorcontrib><creatorcontrib>Plagne, Alain</creatorcontrib><creatorcontrib>Salomon, Julien</creatorcontrib><title>Parallel approximation of the exponential of Hermitian matrices</title><description>In this work, we consider a rational approximation of the exponential
function to design an algorithm for computing matrix exponential in the
Hermitian case. Using partial fraction decomposition, we obtain a
parallelizable method, where the computation reduces to independent resolutions
of linear systems. We analyze the effects of rounding errors on the accuracy of
our algorithm. We complete this work with numerical tests showing the
efficiency of our method and a comparison of its performances with Krylov
algorithms.</description><subject>Computer Science - Distributed, Parallel, and Cluster Computing</subject><subject>Computer Science - Numerical Analysis</subject><subject>Mathematics - Numerical Analysis</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj82KwjAcxHPxILoP4Mm8QGu-05xExF0XBD14L0n8BwOxLbFIfXuru6dhhmGYH0ILSkpRSUlWNg_xUTJOVEmV1tUUrU8225QgYdt1uR3izfaxbXAbcH8FDEPXNtD00aZ3tId8i6Np8FjL0cN9jibBpjt8_esMnb935-2-OBx_frebQ2GVrgphiOROOGJ8UEFzbxwFVSlhvFOeMU4dD9JTqqhkhLgL-EvQwoB3DIIJfIaWf7MfgrrL48_8rN8k9YeEvwArY0Rg</recordid><startdate>20230629</startdate><enddate>20230629</enddate><creator>Hecht, Frédéric</creator><creator>Kaber, Sidi-Mahmoud</creator><creator>Perrin, Lucas</creator><creator>Plagne, Alain</creator><creator>Salomon, Julien</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20230629</creationdate><title>Parallel approximation of the exponential of Hermitian matrices</title><author>Hecht, Frédéric ; Kaber, Sidi-Mahmoud ; Perrin, Lucas ; Plagne, Alain ; Salomon, Julien</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a678-49053b4b09cf6f73c9b1e68649cb6c2231b3f5c11615200bdecdf749ecb2ef9f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Computer Science - Distributed, Parallel, and Cluster Computing</topic><topic>Computer Science - Numerical Analysis</topic><topic>Mathematics - Numerical Analysis</topic><toplevel>online_resources</toplevel><creatorcontrib>Hecht, Frédéric</creatorcontrib><creatorcontrib>Kaber, Sidi-Mahmoud</creatorcontrib><creatorcontrib>Perrin, Lucas</creatorcontrib><creatorcontrib>Plagne, Alain</creatorcontrib><creatorcontrib>Salomon, Julien</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Hecht, Frédéric</au><au>Kaber, Sidi-Mahmoud</au><au>Perrin, Lucas</au><au>Plagne, Alain</au><au>Salomon, Julien</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Parallel approximation of the exponential of Hermitian matrices</atitle><date>2023-06-29</date><risdate>2023</risdate><abstract>In this work, we consider a rational approximation of the exponential
function to design an algorithm for computing matrix exponential in the
Hermitian case. Using partial fraction decomposition, we obtain a
parallelizable method, where the computation reduces to independent resolutions
of linear systems. We analyze the effects of rounding errors on the accuracy of
our algorithm. We complete this work with numerical tests showing the
efficiency of our method and a comparison of its performances with Krylov
algorithms.</abstract><doi>10.48550/arxiv.2306.16778</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Distributed, Parallel, and Cluster Computing Computer Science - Numerical Analysis Mathematics - Numerical Analysis |
| title | Parallel approximation of the exponential of Hermitian matrices |
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