A new integrable convergence acceleration algorithm for computing Brezinski-Durbin-Redivo-Zaglia's sequence transformation via pfaffians | |
Chang, Xiang-Ke1; He, Yi3; Hu, Xing-Biao1,2; Li, Shi-Hao1,2 | |
刊名 | NUMERICAL ALGORITHMS |
2018-05-01 | |
卷号 | 78期号:1页码:87-106 |
关键词 | Convergence Acceleration Algorithm Sequence Transformation Pfaffian Identities |
ISSN号 | 1017-1398 |
DOI | 10.1007/s11075-017-0368-z |
文献子类 | Article |
英文摘要 | In the literature, most known sequence transformations can be written as a ratio of two determinants. But, it is not always this case. One exception is that the sequence transformation proposed by Brezinski, Durbin, and Redivo-Zaglia cannot be expressed as a ratio of two determinants. Motivated by this, we will introduce a new algebraic tool-pfaffians, instead of determinants in the paper. It turns out that Brezinski-Durbin-Redivo-Zaglia's transformation can be expressed as a ratio of two pfaffians. To the best of our knowledge, this is the first time to introduce pfaffians in the expressions of sequence transformations. Furthermore, an extended transformation of high order is presented in terms of pfaffians and a new convergence acceleration algorithm for implementing the transformation is constructed. Then, the Lax pair of the recursive algorithm is obtained which implies that the algorithm is integrable. Numerical examples with applications of the algorithm are also presented. |
WOS关键词 | LOTKA-VOLTERRA SYSTEM ; MULTISTEP EPSILON-ALGORITHM ; SHANKS TRANSFORMATION ; TODA MOLECULE ; COMPUTATION ; EQUATION ; LATTICE ; LAPLACE |
WOS研究方向 | Mathematics |
语种 | 英语 |
出版者 | SPRINGER |
WOS记录号 | WOS:000430408100005 |
资助机构 | National Natural Science Foundation of China(11331008 ; National Natural Science Foundation of China(11331008 ; 11371251 ; 11371251 ; 11201469 ; 11201469 ; 11571358) ; 11571358) ; National Natural Science Foundation of China(11331008 ; National Natural Science Foundation of China(11331008 ; 11371251 ; 11371251 ; 11201469 ; 11201469 ; 11571358) ; 11571358) ; National Natural Science Foundation of China(11331008 ; National Natural Science Foundation of China(11331008 ; 11371251 ; 11371251 ; 11201469 ; 11201469 ; 11571358) ; 11571358) ; National Natural Science Foundation of China(11331008 ; National Natural Science Foundation of China(11331008 ; 11371251 ; 11371251 ; 11201469 ; 11201469 ; 11571358) ; 11571358) |
内容类型 | 期刊论文 |
源URL | [http://ir.wipm.ac.cn/handle/112942/12926] |
专题 | 中国科学院武汉物理与数学研究所 |
通讯作者 | He, Yi; Li, Shi-Hao |
作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100090, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Hubei, Peoples R China |
推荐引用方式 GB/T 7714 | Chang, Xiang-Ke,He, Yi,Hu, Xing-Biao,et al. A new integrable convergence acceleration algorithm for computing Brezinski-Durbin-Redivo-Zaglia's sequence transformation via pfaffians[J]. NUMERICAL ALGORITHMS,2018,78(1):87-106. |
APA | Chang, Xiang-Ke,He, Yi,Hu, Xing-Biao,&Li, Shi-Hao.(2018).A new integrable convergence acceleration algorithm for computing Brezinski-Durbin-Redivo-Zaglia's sequence transformation via pfaffians.NUMERICAL ALGORITHMS,78(1),87-106. |
MLA | Chang, Xiang-Ke,et al."A new integrable convergence acceleration algorithm for computing Brezinski-Durbin-Redivo-Zaglia's sequence transformation via pfaffians".NUMERICAL ALGORITHMS 78.1(2018):87-106. |
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