On a structure-preserving matrix factorization for the determinants of cyclic pentadiagonal Toeplitz matrices
In recent years, a number of numerical algorithms of O ( n ) for computing the determinants of cyclic pentadiagonal matrices have been developed. In this paper, a cost-efficient numerical algorithm for the determinant of an n -by- n cyclic pentadiagonal Toeplitz matrix is proposed whose computationa...
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Veröffentlicht in: | Journal of mathematical chemistry 2019-09, Vol.57 (8), p.2007-2017 |
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container_end_page | 2017 |
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container_issue | 8 |
container_start_page | 2007 |
container_title | Journal of mathematical chemistry |
container_volume | 57 |
creator | Jia, Ji-Teng |
description | In recent years, a number of numerical algorithms of
O
(
n
) for computing the determinants of cyclic pentadiagonal matrices have been developed. In this paper, a cost-efficient numerical algorithm for the determinant of an
n
-by-
n
cyclic pentadiagonal Toeplitz matrix is proposed whose computational cost is estimated at
O
(
log
n
)
. The algorithm is based on a structure-preserving matrix factorization and a three-term recurrence relation. We provide some numerical results with simulations in Matlab implementation in order to demonstrate the accuracy and effectiveness of the proposed algorithm, and its competitiveness with other existing algorithms. |
doi_str_mv | 10.1007/s10910-019-01053-w |
format | Article |
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O
(
n
) for computing the determinants of cyclic pentadiagonal matrices have been developed. In this paper, a cost-efficient numerical algorithm for the determinant of an
n
-by-
n
cyclic pentadiagonal Toeplitz matrix is proposed whose computational cost is estimated at
O
(
log
n
)
. The algorithm is based on a structure-preserving matrix factorization and a three-term recurrence relation. We provide some numerical results with simulations in Matlab implementation in order to demonstrate the accuracy and effectiveness of the proposed algorithm, and its competitiveness with other existing algorithms.</description><identifier>ISSN: 0259-9791</identifier><identifier>EISSN: 1572-8897</identifier><identifier>DOI: 10.1007/s10910-019-01053-w</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Algorithms ; Chemistry ; Chemistry and Materials Science ; Computer simulation ; Determinants ; Factorization ; Ion migration ; Math. Applications in Chemistry ; Numerical analysis ; Original Paper ; Physical Chemistry ; Theoretical and Computational Chemistry</subject><ispartof>Journal of mathematical chemistry, 2019-09, Vol.57 (8), p.2007-2017</ispartof><rights>Springer Nature Switzerland AG 2019</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-2473cd93bea20b4a4477a54ed503d8edde953b629a779e0bb5ada8cdba35b36e3</citedby><cites>FETCH-LOGICAL-c319t-2473cd93bea20b4a4477a54ed503d8edde953b629a779e0bb5ada8cdba35b36e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10910-019-01053-w$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10910-019-01053-w$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>Jia, Ji-Teng</creatorcontrib><title>On a structure-preserving matrix factorization for the determinants of cyclic pentadiagonal Toeplitz matrices</title><title>Journal of mathematical chemistry</title><addtitle>J Math Chem</addtitle><description>In recent years, a number of numerical algorithms of
O
(
n
) for computing the determinants of cyclic pentadiagonal matrices have been developed. In this paper, a cost-efficient numerical algorithm for the determinant of an
n
-by-
n
cyclic pentadiagonal Toeplitz matrix is proposed whose computational cost is estimated at
O
(
log
n
)
. The algorithm is based on a structure-preserving matrix factorization and a three-term recurrence relation. We provide some numerical results with simulations in Matlab implementation in order to demonstrate the accuracy and effectiveness of the proposed algorithm, and its competitiveness with other existing algorithms.</description><subject>Algorithms</subject><subject>Chemistry</subject><subject>Chemistry and Materials Science</subject><subject>Computer simulation</subject><subject>Determinants</subject><subject>Factorization</subject><subject>Ion migration</subject><subject>Math. Applications in Chemistry</subject><subject>Numerical analysis</subject><subject>Original Paper</subject><subject>Physical Chemistry</subject><subject>Theoretical and Computational Chemistry</subject><issn>0259-9791</issn><issn>1572-8897</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLxDAUhYMoOI7-AVcB19WkaSbJUsQXCG7GdbhNbscMM01NMr5-vdUK7lxczuZ8h8tHyCln55wxdZE5M5xVjJvxmBTV2x6ZcanqSmuj9smM1dJURhl-SI5yXjPGjF7oGdk-9hRoLmnnyi5hNSTMmF5Dv6JbKCm80w5ciSl8Qgmxp11MtDwj9VgwbUMPfck0dtR9uE1wdMC-gA-wij1s6DLisAnlc5pymI_JQQebjCe_OSdPN9fLq7vq4fH2_uryoXKCm1LVjRLOG9Ei1KxtoGmUAtmgl0x4jd6jkaJd1AaUMsjaVoIH7XwLQrZigWJOzqbdIcWXHeZi13GXxpeyrWulmdZyIcdWPbVcijkn7OyQwhbSh-XMfmu1k1Y7arU_Wu3bCIkJymO5X2H6m_6H-gK5jn7K</recordid><startdate>20190901</startdate><enddate>20190901</enddate><creator>Jia, Ji-Teng</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20190901</creationdate><title>On a structure-preserving matrix factorization for the determinants of cyclic pentadiagonal Toeplitz matrices</title><author>Jia, Ji-Teng</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-2473cd93bea20b4a4477a54ed503d8edde953b629a779e0bb5ada8cdba35b36e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Algorithms</topic><topic>Chemistry</topic><topic>Chemistry and Materials Science</topic><topic>Computer simulation</topic><topic>Determinants</topic><topic>Factorization</topic><topic>Ion migration</topic><topic>Math. Applications in Chemistry</topic><topic>Numerical analysis</topic><topic>Original Paper</topic><topic>Physical Chemistry</topic><topic>Theoretical and Computational Chemistry</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jia, Ji-Teng</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of mathematical chemistry</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Jia, Ji-Teng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On a structure-preserving matrix factorization for the determinants of cyclic pentadiagonal Toeplitz matrices</atitle><jtitle>Journal of mathematical chemistry</jtitle><stitle>J Math Chem</stitle><date>2019-09-01</date><risdate>2019</risdate><volume>57</volume><issue>8</issue><spage>2007</spage><epage>2017</epage><pages>2007-2017</pages><issn>0259-9791</issn><eissn>1572-8897</eissn><abstract>In recent years, a number of numerical algorithms of
O
(
n
) for computing the determinants of cyclic pentadiagonal matrices have been developed. In this paper, a cost-efficient numerical algorithm for the determinant of an
n
-by-
n
cyclic pentadiagonal Toeplitz matrix is proposed whose computational cost is estimated at
O
(
log
n
)
. The algorithm is based on a structure-preserving matrix factorization and a three-term recurrence relation. We provide some numerical results with simulations in Matlab implementation in order to demonstrate the accuracy and effectiveness of the proposed algorithm, and its competitiveness with other existing algorithms.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s10910-019-01053-w</doi><tpages>11</tpages></addata></record> |
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subjects | Algorithms Chemistry Chemistry and Materials Science Computer simulation Determinants Factorization Ion migration Math. Applications in Chemistry Numerical analysis Original Paper Physical Chemistry Theoretical and Computational Chemistry |
title | On a structure-preserving matrix factorization for the determinants of cyclic pentadiagonal Toeplitz matrices |
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