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

doi:10.1007/s11075-017-0368-z

	A new integrable convergence acceleration algorithm for computing Brezinski-Durbin-Redivo-Zaglia's sequence transformation via pfaffians
	Chang, Xiang-Ke1 ; He, Yi 2; Hu, Xing-Biao1,3 ; Li, Shi-Hao 1,3
	2018-05-01
发表期刊	NUMERICAL ALGORITHMS
ISSN	1017-1398
卷号	78 期号:1 页码:87-106
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.
关键词	Convergence acceleration algorithm Sequence transformation Pfaffian identities
DOI	10.1007/s11075-017-0368-z
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000430408100005
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29996
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.