ダメ人間のためのreliableの6つのコツ

Reliable Methods for Computer SimulationError Control and Posteriori Estimates【電子書籍】[ Pekka Neittaanm?ki ]

＜p＞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.＜/p＞ ＜p＞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.＜/p＞ ＜p＞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.＜/p＞ ＜p＞・ computable bounds of approximation errors＜br /＞ ・ checking algorithms＜br /＞ ・ iteration processes＜br /＞ ・ finite element methods＜br /＞ ・ elliptic type problems＜br /＞ ・ nonlinear variational problems＜br /＞ ・ variational inequalities＜/p＞画面が切り替わりますので、しばらくお待ち下さい。

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