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Titlebook: Numerical Toolbox for Verified Computing I; Basic Numerical Prob Ulrich Kulisch,Rolf Hammer,Matthias Hocks Book 1993 Springer-Verlag Berlin

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书目名称Numerical Toolbox for Verified Computing I
副标题Basic Numerical Prob
编辑Ulrich Kulisch,Rolf Hammer,Matthias Hocks
视频video
丛书名称Springer Series in Computational Mathematics
图书封面Titlebook: Numerical Toolbox for Verified Computing I; Basic Numerical Prob Ulrich Kulisch,Rolf Hammer,Matthias Hocks Book 1993 Springer-Verlag Berlin
描述As suggested by the title of this book Numerical Toolbox for Verified Computing, we present an extensive set of sophisticated tools to solve basic numerical problems with a verification of the results. We use the features of the scientific computer language PASCAL-XSC to offer modules that can be combined by the reader to his/her individual needs. Our overriding concern is reliability - the automatic verification of the result a computer returns for a given problem. All algorithms we present are influenced by this central concern. We must point out that there is no relationship between our methods of numerical result verification and the methods of program verification to prove the correctness of an imple~entation for a given algorithm. This book is the first to offer a general discussion on • arithmetic and computational reliability, • analytical mathematics and verification techniques, • algorithms, and • (most importantly) actual implementations in the form of working computer routines. Our task has been to find the right balance among these ingredients for each topic. For some topics, we have placed a little more emphasis on the algorithms. For other topics, where the mathemati
出版日期Book 1993
关键词PASCAL-XSC; Vereinfachung der Programmierung; Verified Computing; algorithms; automatische Ergebnisverii
版次1
doihttps://doi.org/10.1007/978-3-642-78423-1
isbn_softcover978-3-642-78425-5
isbn_ebook978-3-642-78423-1Series ISSN 0179-3632 Series E-ISSN 2198-3712
issn_series 0179-3632
copyrightSpringer-Verlag Berlin Heidelberg 1993
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Numerical Toolbox for Verified Computing I978-3-642-78423-1Series ISSN 0179-3632 Series E-ISSN 2198-3712
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The Features of PASCAL-XSCIn this chapter, we give a short overview of the new concepts of the programming language PASCAL-XSC, a universal PASCAL e.tension for .cientific .omputation with extensive predefined modules for scientific computation. For a complete language reference and examples, we refer to [44] and [45].
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Linear Systems of EquationsFinding the solution of a linear system of equations is one of the basic problems in numerical algebra. We will develop a verification algorithm for square systems with full matrix based on a Newton-like method for an equivalent fixed-point problem.
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Linear OptimizationA linear programming problem consists of a linear function to be maximized (or minimized) subject to linear equality and inequality constraints. Any linear program (LP) can be put by well-known transformations into standard form.where . is a real . x . matrix, . ., c . ., and .. The input data of (11.1) are given by the triple . = (.) .
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Introduction provide theory, algorithmic descriptions, and implementations for methods to solve some basic numerical problems in a reliable way. Also, this book can help you learn how to develop such methods and how to proceed for other problems beyond the scope of the book.
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