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作者 Neittaanmäki, P. (Pekka)
書名 Reliable methods for computer simulation [electronic resource] : error control and a posteriori estimates / P. Neittaanmäki and S. Repin
出版項 Amsterdam ; San Diego, CA : Elsevier, 2004
國際標準書號 9780444513762
book jacket
說明 x, 305 p. : ill. ; 24 cm
系列 Studies in mathematics and its applications ; v. 33
附註 Includes bibliographical references (p. 281-299) and index
Contents -- 1. Introduction. -- 2. Mathematical background. -- 3. A posteriori estimates for iteration methods. -- 4. A posteriori estimates for finite element approximations. -- 5. Foundations of duality theory. -- 6. Two-sided a posteriori estimates for linear elliptic problems. -- 7. A posteriori estimates for nonlinear variational problems. -- 8. A posteriori estimates for variational inequalities. -- Bibliography. -- Notation. -- Index
Electronic reproduction. Amsterdam : Elsevier Science & Technology, 2007. Mode of access: World Wide Web. System requirements: Web browser. Title from title screen (viewed on July 25, 2007). Access may be restricted to users at subscribing institutions
Recent decades have seen a very rapid success in developing numerical methods based on explicit control over approximation errors. It may be said that nowadays a new direction is forming in numerical analysis, the main goal of which is to develop methods ofreliable computations. In general, a reliable numerical method must solve two basic problems: (a) generate a sequence of approximations that converges to a solution and (b) verify the accuracy of these approximations. A computer code for such a method must consist of two respective blocks: solver and checker. In this book, we are chiefly concerned with the problem (b) and try to present the main approaches developed for a posteriori error estimation in various problems. The authors try to retain a rigorous mathematical style, however, proofs are constructive whenever possible and additional mathematical knowledge is presented when necessary. The book contains a number of new mathematical results and lists a posteriori error estimation methods that have been developed in the very recent time. computable bounds of approximation errors checking algorithms iteration processes finite element methods elliptic type problems nonlinear variational problems variational inequalities
鏈接 Original 0444513760 9780444513762 (DLC) 2006277839 (OCoLC)56463686
主題 Numerical analysis
Error-correcting codes (Information theory)
Approximation theory
Electronic books. local
Alt Author Repin, Sergey I
ScienceDirect (Online service)
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