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A new integrable convergence acceleration algorithm for computing Brezinski-Durbin-Redivo-Zaglia's sequence transformation via pfaffians

文献类型：期刊论文

作者Chang, Xiang-Ke1; He, Yi2; Hu, Xing-Biao1,3; Li, Shi-Hao1,3
刊名NUMERICAL ALGORITHMS
出版日期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
DOI10.1007/s11075-017-0368-z
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.
资助项目National Natural Science Foundation of China[11331008] ; National Natural Science Foundation of China[11371251] ; National Natural Science Foundation of China[11201469] ; National Natural Science Foundation of China[11571358]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000430408100005
出版者SPRINGER
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/29995]  
专题计算数学与科学工程计算研究所
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.Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Hubei, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, 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.

入库方式： OAI收割

来源：数学与系统科学研究院

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