Improved global algorithms for maximal eigenpair
This paper is a continuation of our previous paper [Front. Math. China, 2017, 12(5): 1023–1043] where global algorithms for computing the maximal eigenpair were introduced in a rather general setup. The efficiency of the global algorithms is improved in this paper in terms of a good use of power ite...
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| Published in | Frontiers of Mathematics Vol. 14; no. 6; pp. 1077 - 1116 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Beijing
Higher Education Press
01.12.2019
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1673-3452 2731-8648 1673-3576 2731-8656 |
| DOI | 10.1007/s11464-019-0799-z |
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| Abstract | This paper is a continuation of our previous paper [Front. Math. China, 2017, 12(5): 1023–1043] where global algorithms for computing the maximal eigenpair were introduced in a rather general setup. The efficiency of the global algorithms is improved in this paper in terms of a good use of power iteration and two quasi-symmetric techniques. Finally, the new algorithms are applied to Hua’s economic optimization model. |
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| AbstractList | This paper is a continuation of our previous paper [Front. Math. China, 2017, 12(5): 1023–1043] where global algorithms for computing the maximal eigenpair were introduced in a rather general setup. The efficiency of the global algorithms is improved in this paper in terms of a good use of power iteration and two quasi-symmetric techniques. Finally, the new algorithms are applied to Hua’s economic optimization model. |
| Author | Chen, Mu-Fa Li, Yue-Shuang |
| Author_xml | – sequence: 1 givenname: Mu-Fa surname: Chen fullname: Chen, Mu-Fa email: mfchen@bnu.edu.cn organization: School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems (Beijing Normal University), Ministry of Education – sequence: 2 givenname: Yue-Shuang surname: Li fullname: Li, Yue-Shuang email: liyueshuang@mail.bnu.edu.cn organization: School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems (Beijing Normal University), Ministry of Education |
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| References | Chen (CR3) 2016; 11 Chen (CR7) 2017; 41 Hua (CR15) 1985; 9 You, Shu, Yuan (CR19) 2017; 65 Chen (CR2) 2005 Hua (CR14) 1984; 12 Wang (CR18) 1996 Chen (CR8) 2018; 13 Dynkin (CR11) 1965 Chen (CR4) 2017; 12 Chen (CR5) 2017; 46 Hua, Hua (CR16) 1985; 8 Chen, Mao (CR10) 2007 Chen, Li (CR9) 2019; 14 Hall, Porsching (CR12) 1969; 36 Hua, Yang (CR17) 2010 Zhang (CR20) 2018; 13 Butler, Siegel (CR1) 2013; 439 Hou, Guo (CR13) 1978 Chen, Yue, Li, Jin, Ma (CR6) 2017 B K Butler (799_CR1) 2013; 439 M F Chen (799_CR4) 2017; 12 M F Chen (799_CR5) 2017; 46 M F Chen (799_CR10) 2007 Y H Zhang (799_CR20) 2018; 13 M F Chen (799_CR6) 2017 M F Chen (799_CR9) 2019; 14 Z T Hou (799_CR13) 1978 L H You (799_CR19) 2017; 65 M F Chen (799_CR3) 2016; 11 Z K Wang (799_CR18) 1996 E B Dynkin (799_CR11) 1965 M F Chen (799_CR7) 2017; 41 L K Hua (799_CR16) 1985; 8 M F Chen (799_CR2) 2005 C A Hall (799_CR12) 1969; 36 M F Chen (799_CR8) 2018; 13 L K Hua (799_CR15) 1985; 9 L K Hua (799_CR14) 1984; 12 L K Hua (799_CR17) 2010 |
| References_xml | – volume: 12 start-page: 705 year: 1984 end-page: 709 ident: CR14 article-title: Mathematical theory of large-scale optimization of planned economy (I) publication-title: Chin Sci Bull doi: 10.1360/csb1984-29-12-705 – volume: 439 start-page: 1468 issue: 5 year: 2013 end-page: 1478 ident: CR1 article-title: Sharp bounds on the spectral radius of nonnegative matrices and digraphs publication-title: Linear Algebra Appl doi: 10.1016/j.laa.2013.04.029 – year: 1978 ident: CR13 publication-title: Time-Homogeneous Markov Processes with Countable State Space – volume: 11 start-page: 1379 issue: 6 year: 2016 end-page: 1418 ident: CR3 article-title: Efficient initials for computing the maximal eigenpair publication-title: Front Math China doi: 10.1007/s11464-016-0573-4 – volume: 9 start-page: 641 year: 1985 end-page: 645 ident: CR15 article-title: Mathematical theory of large-scale optimization of planned economy (X) publication-title: Chin Sci Bull doi: 10.1360/csb1985-30-9-641 – start-page: 39 year: 2010 end-page: 53 ident: CR17 article-title: Mathematical theory on economic optimal balance publication-title: Collected Works by L K Hua (Applied Math II) – volume: 13 start-page: 1215 issue: 5 year: 2018 end-page: 1243 ident: CR20 article-title: Criteria on ergodicity and strong ergodicity of single death processes publication-title: Front Math China doi: 10.1007/s11464-018-0722-z – volume: 12 start-page: 1023 issue: 5 year: 2017 end-page: 1043 ident: CR4 article-title: Global algorithms for maximal eigenpair publication-title: Front Math China doi: 10.1007/s11464-017-0658-8 – start-page: 312 year: 2017 end-page: 329 ident: CR6 article-title: Trilogy on computing maximal eigenpair publication-title: Queueing Theory and Network Applications (QTNA 2017) doi: 10.1007/978-3-319-68520-5_19 – volume: 8 start-page: 30 year: 1985 end-page: 33 ident: CR16 article-title: Study on real square matrix with positive left- and right-eigenvectors simultaneous publication-title: Mathematics Bull – volume: 46 start-page: 281 issue: 4 year: 2017 end-page: 297 ident: CR5 article-title: The charming leading eigenpair publication-title: Adv Math (China) – volume: 36 start-page: 159 issue: 1 year: 1969 end-page: 164 ident: CR12 article-title: Bounds for the maximal eigenvalue of a nonnegative irreducible matrix publication-title: Duke Math J doi: 10.1215/S0012-7094-69-03621-7 – year: 1996 ident: CR18 publication-title: General Theory of Stochastic Processes – volume: 41 start-page: 13 issue: 3 year: 2017 end-page: 25 ident: CR7 article-title: The optimal search problem—begins with the loss of Malaysia Airlines publication-title: Math Media – volume: 65 start-page: 113 issue: 1 year: 2017 end-page: 128 ident: CR19 article-title: Sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix and its applications publication-title: Linear Multilinear Algebra doi: 10.1080/03081087.2016.1168355 – year: 2007 ident: CR10 publication-title: Introduction to Stochastic Processes – volume: 13 start-page: 1267 issue: 6 year: 2018 end-page: 1311 ident: CR8 article-title: Hermitizable, isospectral complex matrices or differential operators publication-title: Front Math China doi: 10.1007/s11464-018-0716-x – year: 2005 ident: CR2 publication-title: Eigenvalues, Inequalities, and Ergodic Theory – volume: 14 start-page: 493 issue: 3 year: 2019 end-page: 519 ident: CR9 article-title: Development of powerful algorithm for maximal eigenpair publication-title: Front Math China doi: 10.1007/s11464-019-0769-5 – year: 1965 ident: CR11 publication-title: Markov Processes doi: 10.1007/978-3-662-00031-1 – volume: 11 start-page: 1379 issue: 6 year: 2016 ident: 799_CR3 publication-title: Front Math China doi: 10.1007/s11464-016-0573-4 – volume: 65 start-page: 113 issue: 1 year: 2017 ident: 799_CR19 publication-title: Linear Multilinear Algebra doi: 10.1080/03081087.2016.1168355 – volume: 41 start-page: 13 issue: 3 year: 2017 ident: 799_CR7 publication-title: Math Media – volume-title: Introduction to Stochastic Processes year: 2007 ident: 799_CR10 – volume-title: General Theory of Stochastic Processes year: 1996 ident: 799_CR18 – volume-title: Markov Processes year: 1965 ident: 799_CR11 doi: 10.1007/978-3-662-00031-1 – start-page: 39 volume-title: Collected Works by L K Hua (Applied Math II) year: 2010 ident: 799_CR17 – volume-title: Eigenvalues, Inequalities, and Ergodic Theory year: 2005 ident: 799_CR2 – volume: 14 start-page: 493 issue: 3 year: 2019 ident: 799_CR9 publication-title: Front Math China doi: 10.1007/s11464-019-0769-5 – volume-title: Time-Homogeneous Markov Processes with Countable State Space year: 1978 ident: 799_CR13 – volume: 12 start-page: 1023 issue: 5 year: 2017 ident: 799_CR4 publication-title: Front Math China doi: 10.1007/s11464-017-0658-8 – volume: 13 start-page: 1267 issue: 6 year: 2018 ident: 799_CR8 publication-title: Front Math China doi: 10.1007/s11464-018-0716-x – 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| Title | Improved global algorithms for maximal eigenpair |
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