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＜電子ブック＞
Introduction to Numerical Analysis / by J. Stoer, R. Bulirsch

版	1st ed. 1980.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	1980
本文言語	英語
大きさ	IX, 609 p : online resource
著者標目	*Stoer, J author Bulirsch, R author SpringerLink (Online service)
件　名	LCSH:Numerical analysis FREE:Numerical Analysis
一般注記	1 Error Analysis -- 2 Interpolation -- 3 Topics in Integration -- 4 Systems of Linear Equations -- 5 Finding Zeros and Minimum Points by Iterative Methods -- 6 Eigenvalue Problems -- 7 Ordinary Differential Equations -- 8 Iterative Methods for the Solution of Large Systems of Linear Equations. Some Further Methods -- General Literature on Numerical Methods This book is based on a one-year introductory course on numerical analysis given by the authors at several universities in Germany and the United States. The authors concentrate on methods which can be worked out on a digital computer. For important topics, algorithmic descriptions (given more or less formally in ALGOL 60), as well as thorough but concise treatments of their theoretical founda­ tions, are provided. Where several methods for solving a problem are presented, comparisons of their applicability and limitations are offered. Each comparison is based on operation counts, theoretical properties such as convergence rates, and, more importantly, the intrinsic numerical properties that account for the reliability or unreliability of an algorithm. Within this context, the introductory chapter on error analysis plays a special role because it precisely describes basic concepts, such as the numerical stability of algorithms, that are indispensable in the thorough treatment of numerical questions. The remaining seven chapters are devoted to describing numerical methods in various contexts. In addition to covering standard topics, these chapters encom­ pass some special subjects not usually found in introductions to numerical analysis. Chapter 2, which discusses interpolation, gives an account of modem fast Fourier transform methods. In Chapter 3, extrapolation techniques for spe~d­ ing up the convergence of discretization methods in connection with Romberg integration are explained at length HTTP:URL=https://doi.org/10.1007/978-1-4757-5592-3

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