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Titlebook: Introduction to Numerical Analysis; J. Stoer,R. Bulirsch Textbook 19801st edition Springer Science+Business Media New York 1980 Analysis.E

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书目名称Introduction to Numerical Analysis
编辑J. Stoer,R. Bulirsch
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图书封面Titlebook: Introduction to Numerical Analysis;  J. Stoer,R. Bulirsch Textbook 19801st edition Springer Science+Business Media New York 1980 Analysis.E
描述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 n
出版日期Textbook 19801st edition
关键词Analysis; Eigenvalue; algorithms; boundary element method; calculus; convergence; differential equation; in
版次1
doihttps://doi.org/10.1007/978-1-4757-5592-3
isbn_ebook978-1-4757-5592-3
copyrightSpringer Science+Business Media New York 1980
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Springer Science+Business Media New York 1980
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Error Analysis,Assessing the accuracy of the results of calculations is a paramount goal in numerical analysis. One distinguishes several kinds of errors which may limit this accuracy:
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Interpolation,Consider a family of functions of a single variable ., . having . + 1 parameters .., ... , .., whose values characterize the individual functions in this family.
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Topics in Integration,Calculating the definite integral of a given real function .), ., is a classic problem. For some simple integrands . (.), the indefinite integral . can be obtained in closed form as an algebraic expression in . and well-known transcendental functions of ..
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Eigenvalue Problems,Many practical problems in engineering and physics lead to eigenvalue problems. Typically, in all these problems, an overdetermined system of equations is given, say . + 1 equations for . unknowns .. ... , .. of the form.
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Ordinary Differential Equations,Many problems in applied mathematics lead to ordinary differential equations. In the simplest case one seeks a differentiable function .) of one real variable ., whose derivative .) is to satisfy an equation of the form .)), or more briefly, . one then speaks of an ..
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https://doi.org/10.1007/978-1-4757-5592-3Analysis; Eigenvalue; algorithms; boundary element method; calculus; convergence; differential equation; in
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