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A new integrable convergence acceleration algorithm for computing Brezinski-Durbin-Redivo-Zaglia's sequence transformation via pfaffians
Chang, Xiang-Ke1; He, Yi2; Hu, Xing-Biao1,3; Li, Shi-Hao1,3
2018-05-01
Source PublicationNUMERICAL ALGORITHMS
ISSN1017-1398
Volume78Issue:1Pages:87-106
AbstractIn 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.
KeywordConvergence acceleration algorithm Sequence transformation Pfaffian identities
DOI10.1007/s11075-017-0368-z
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000430408100005
PublisherSPRINGER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29996
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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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