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Convergence acceleration algorithms related to a generalized E-transformation and its particular cases

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 2013年第2期30卷 263-285页

作者： He, Yi Hu, Xing-Biao Tam, Hon-Wah Tsujimoto, Satoshi Chinese Acad Sci Wuhan Inst Phys & Math Wuhan 430071 Peoples R China Chinese Acad Sci AMSS Inst Computat Math & Sci Engn Comp LSEC Beijing 100190 Peoples R China Hong Kong Baptist Univ Dept Comp Sci Kowloon Tong Hong Kong Peoples R China Kyoto Univ Grad Sch Informat Dept Appl Math & Phys Kyoto 6068501 Japan

In this paper, a generalized E-transformation arising from the study of a generalization of sequence transformations and triangular recursion schemes is proposed. Three new algorithms, namely, the generalized E-algorithm, the generalized FS-algorithm and the generalized hungry type E-algorithm, are constructed for implementing the generalization of the E-transformation. Some convergence results of the generalized E-algorithm are obtained. In addition, some particular cases of the generalized E-transformation and the recursive algorithms for their computation are also studied.

关键词： E-transformation epsilon-algorithm G-algorithm rs-algorithm qd-algorithm

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A generalization of the G-transformation and the related algorithms

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APPLIED NUMERICAL MATHEMATICS 2010年第12期60卷 1221-1230页

作者： Brezinski, Claude He, Yi Hu, Xing-Biao Sun, Jian-Qing Chinese Acad Sci AMSS LSEC Inst Computat Math & Sci Beijing 100190 Peoples R China Univ Sci & Technol Lille CNRS Lab Paul Painleve UFR Math Pures & AppliqueesUMR 8524 F-59655 Villeneuve Dascq France Chinese Acad Sci Grad Sch Beijing 100190 Peoples R China

In this paper, a generalization of the G-transformation is proposed together with the corresponding auxiliary rs-algorithm for implementation. We show that the related generalization of the rs-algorithm is equivalent to a generalized qd-algorithm. Applications of the generalization of the G-transformation to the computation of infinite integrals are also given. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： G-transformation G-algorithm rs-algorithm qd-algorithm

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Retrieval system and dynamic algorithm looking for axioms of notions defined by programs

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Fundamenta Informaticae 1993年第3-4期19卷 275-275页

作者： Biela, A. Department of Mathematics University of Silesia PL-40-007 Katowice Poland

In this paper we shall introduce a formal system of algorithmic logic which enables us to formulate some problems connected with a retrieval system which provides a comprehensive tool in automated theorem proving of theorems consisting of programs, procedures and functions. The procedures and functions may occur in considered theorems while the program of the above mentioned system is being executed. We can get an answer whether some relations defined by programs hold and we can prove functional equations in a dynamic way by looking for a special set of axioms /assumptions/ during the execution of system. We formulate rs-algorithm which enables us to construct the set of axioms for proving some properties of functions and relations defined by programs. By rs-algorithm we get the dynamic process of proving functional equations and we can answer the question whether some relations defined by programs hold. It enables us to solve some problems concerning the correctness of programs. This system can be used for giving an expert appraisement. We shall provide the major structures and a sketch of an implementation of the above formal system.

关键词： algorithmic logic diagram procedures rs-algorithm implementation experimental results

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A generalization of the G-transformation and the related algorithms

A generalization of the <i>G</i>-transformation and the rela...

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Conference on Approximation and Extrapolation of Convergent and Divergent Sequences and Series

关键词： G-transformation G-algorithm rs-algorithm qd-algorithm

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