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Generalized Fractional Algebraic Linear System Solvers
This paper is devoted to the numerical computation of algebraic linear systems involving several matrix power functions; that is finding x solution to ∑ α ∈ R A α x = b . These systems will be referred to as Generalized Fractional Algebraic Linear Systems (GFALS). In this paper, we derive several gr...
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| Published in: | Journal of scientific computing 2022-04, Vol.91 (1), p.25, Article 25 |
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| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c397t-6796120bddb0d46cee07b339ca8ae19086d5fb600edcefc4f09af1f955af8f623 |
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| container_title | Journal of scientific computing |
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| creator | Antoine, X. Lorin, E. |
| description | This paper is devoted to the numerical computation of algebraic linear systems involving several matrix power functions; that is finding
x
solution to
∑
α
∈
R
A
α
x
=
b
. These systems will be referred to as
Generalized Fractional Algebraic Linear Systems
(GFALS). In this paper, we derive several gradient methods for solving these very computationally complex problems, which themselves require the solution to intermiediate
standard Fractional Algebraic Linear Systems
(FALS)
A
α
x
=
b
, with
α
∈
R
+
. The latter usually require the solution to many
classical linear systems
A
x
=
b
. We also show that in some cases, the solution to a GFALS problem can be obtained as the solution to a first-order hyperbolic system of conservation laws. We also discuss the connections between this PDE-approach and gradient-type methods. The convergence analysis is addressed and some numerical experiments are proposed to illustrate and compare the methods which are proposed in this paper. |
| doi_str_mv | 10.1007/s10915-022-01785-z |
| format | article |
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x
solution to
∑
α
∈
R
A
α
x
=
b
. These systems will be referred to as
Generalized Fractional Algebraic Linear Systems
(GFALS). In this paper, we derive several gradient methods for solving these very computationally complex problems, which themselves require the solution to intermiediate
standard Fractional Algebraic Linear Systems
(FALS)
A
α
x
=
b
, with
α
∈
R
+
. The latter usually require the solution to many
classical linear systems
A
x
=
b
. We also show that in some cases, the solution to a GFALS problem can be obtained as the solution to a first-order hyperbolic system of conservation laws. We also discuss the connections between this PDE-approach and gradient-type methods. The convergence analysis is addressed and some numerical experiments are proposed to illustrate and compare the methods which are proposed in this paper.</description><identifier>ISSN: 0885-7474</identifier><identifier>EISSN: 1573-7691</identifier><identifier>DOI: 10.1007/s10915-022-01785-z</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Algorithms ; Analysis of PDEs ; Approximation ; Computational Mathematics and Numerical Analysis ; Conservation laws ; Eigenvalues ; Hyperbolic systems ; Linear systems ; Mathematical analysis ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Methods ; Numerical Analysis ; Partial differential equations ; Theoretical</subject><ispartof>Journal of scientific computing, 2022-04, Vol.91 (1), p.25, Article 25</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022</rights><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022.</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c397t-6796120bddb0d46cee07b339ca8ae19086d5fb600edcefc4f09af1f955af8f623</citedby><cites>FETCH-LOGICAL-c397t-6796120bddb0d46cee07b339ca8ae19086d5fb600edcefc4f09af1f955af8f623</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,27924,27925</link.rule.ids><backlink>$$Uhttps://hal.science/hal-03085997$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Antoine, X.</creatorcontrib><creatorcontrib>Lorin, E.</creatorcontrib><title>Generalized Fractional Algebraic Linear System Solvers</title><title>Journal of scientific computing</title><addtitle>J Sci Comput</addtitle><description>This paper is devoted to the numerical computation of algebraic linear systems involving several matrix power functions; that is finding
x
solution to
∑
α
∈
R
A
α
x
=
b
. These systems will be referred to as
Generalized Fractional Algebraic Linear Systems
(GFALS). In this paper, we derive several gradient methods for solving these very computationally complex problems, which themselves require the solution to intermiediate
standard Fractional Algebraic Linear Systems
(FALS)
A
α
x
=
b
, with
α
∈
R
+
. The latter usually require the solution to many
classical linear systems
A
x
=
b
. We also show that in some cases, the solution to a GFALS problem can be obtained as the solution to a first-order hyperbolic system of conservation laws. We also discuss the connections between this PDE-approach and gradient-type methods. The convergence analysis is addressed and some numerical experiments are proposed to illustrate and compare the methods which are proposed in this paper.</description><subject>Algebra</subject><subject>Algorithms</subject><subject>Analysis of PDEs</subject><subject>Approximation</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Conservation laws</subject><subject>Eigenvalues</subject><subject>Hyperbolic systems</subject><subject>Linear systems</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Methods</subject><subject>Numerical Analysis</subject><subject>Partial differential equations</subject><subject>Theoretical</subject><issn>0885-7474</issn><issn>1573-7691</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kE1Lw0AURQdRsFb_gKuAKxfRN5nM17IUbYWAi-p6mEze1JQ0qTNtof31pkZ05-rB5dwL7xByS-GBAsjHSEFTnkKWpUCl4unxjIwolyyVQtNzMgLVhzKX-SW5inEFAFrpbETEDFsMtqmPWCXPwbpt3bW2SSbNEstga5cUdYs2JItD3OI6WXTNHkO8JhfeNhFvfu6YvD8_vU3nafE6e5lOitQxLbepkFrQDMqqKqHKhUMEWTKmnVUWqQYlKu5LAYCVQ-9yD9p66jXn1isvMjYm98Puh23MJtRrGw6ms7WZTwpzyoCB4lrLPe3Zu4HdhO5zh3FrVt0u9M9Ek2mqGOUcdE9lA-VCF2NA_ztLwZxcmsGl6V2ab5fm2JfYUIo93C4x_E3_0_oCdSN2uQ</recordid><startdate>20220401</startdate><enddate>20220401</enddate><creator>Antoine, X.</creator><creator>Lorin, E.</creator><general>Springer US</general><general>Springer Nature B.V</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>1XC</scope><scope>VOOES</scope></search><sort><creationdate>20220401</creationdate><title>Generalized Fractional Algebraic Linear System Solvers</title><author>Antoine, X. ; Lorin, E.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c397t-6796120bddb0d46cee07b339ca8ae19086d5fb600edcefc4f09af1f955af8f623</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Algebra</topic><topic>Algorithms</topic><topic>Analysis of PDEs</topic><topic>Approximation</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Conservation laws</topic><topic>Eigenvalues</topic><topic>Hyperbolic systems</topic><topic>Linear systems</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Methods</topic><topic>Numerical Analysis</topic><topic>Partial differential equations</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Antoine, X.</creatorcontrib><creatorcontrib>Lorin, E.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Journal of scientific computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Antoine, X.</au><au>Lorin, E.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Generalized Fractional Algebraic Linear System Solvers</atitle><jtitle>Journal of scientific computing</jtitle><stitle>J Sci Comput</stitle><date>2022-04-01</date><risdate>2022</risdate><volume>91</volume><issue>1</issue><spage>25</spage><pages>25-</pages><artnum>25</artnum><issn>0885-7474</issn><eissn>1573-7691</eissn><abstract>This paper is devoted to the numerical computation of algebraic linear systems involving several matrix power functions; that is finding
x
solution to
∑
α
∈
R
A
α
x
=
b
. These systems will be referred to as
Generalized Fractional Algebraic Linear Systems
(GFALS). In this paper, we derive several gradient methods for solving these very computationally complex problems, which themselves require the solution to intermiediate
standard Fractional Algebraic Linear Systems
(FALS)
A
α
x
=
b
, with
α
∈
R
+
. The latter usually require the solution to many
classical linear systems
A
x
=
b
. We also show that in some cases, the solution to a GFALS problem can be obtained as the solution to a first-order hyperbolic system of conservation laws. We also discuss the connections between this PDE-approach and gradient-type methods. The convergence analysis is addressed and some numerical experiments are proposed to illustrate and compare the methods which are proposed in this paper.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10915-022-01785-z</doi><oa>free_for_read</oa></addata></record> |
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| issn | 0885-7474 1573-7691 |
| language | eng |
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| source | Springer Link |
| subjects | Algebra Algorithms Analysis of PDEs Approximation Computational Mathematics and Numerical Analysis Conservation laws Eigenvalues Hyperbolic systems Linear systems Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Methods Numerical Analysis Partial differential equations Theoretical |
| title | Generalized Fractional Algebraic Linear System Solvers |
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