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" Numerical Toolbox for Verified Computing I : "
by Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks.
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BL
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| Record Number
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753864
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b573825
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| Main Entry
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by Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks.
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| Title & Author
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Numerical Toolbox for Verified Computing I : : Basic Numerical Problems Theory, Algorithms, and Pascal-XSC Programs\ by Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks.
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| Publication Statement
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Berlin, Heidelberg : Springer Berlin Heidelberg, 1993
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| Series Statement
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Springer series in computational mathematics, 21.
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| Page. NO
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(xv, 339 pages 28 illustrations)
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| ISBN
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3642784232
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: 9783642784231
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| Contents
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1 Introduction --; 1 Introduction --; I Preliminaries --; 2 The Features of PASCAL --; XSC --; 3 Mathematical Preliminaries --; II One-Dimensional Problems --; 4 Evaluation of Polynomials --; 5 Automatic Differentiation --; 6 Nonlinear Equations in One Variable --; 7 Global Optimization --; 8 Evaluation of Arithmetic Expressions --; 9 Zeros of Complex Polynomials --; III Multi-Dimensional Problems --; 10 Linear Systems of Equations --; 11 Linear Optimization --; 12 Automatic Differentiation for Gradients, Jacobians, and Hessians --; 13 Nonlinear Systems of Equations --; 14 Global Optimization --; A Utility Modules --; A.l Module b_util --; A.2 Module r_util --; A.3 Module i_util --; A.4 Module mvi_util --; Index of Special Symbols.
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| Abstract
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This book presents an extensive set of sophisticated tools to solve numerical problems with a verification of the results using the features of the scientific computer language PASCAL-XSC. The overriding concern of this book is reliability - the automatic verification of the result a computer returns for a given problem. 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. In each chapter, examples, exercises, and numerical results demonstrate the application of the routines presented. It is not assumed that the reader has any prior formal knowledge of numerical verification or any familiarity with interval analysis. Some of the subjects that the book covers in detail are not usually found in standard numerical analysis texts. This book is intended primarily as a reference text, however, it can also be used as a textbook for an advanced course in scientific computation with automatic result verification.
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| Subject
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Computer science.
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Mathematics.
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Numerical analysis.
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| LC Classification
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QA300.B985 1993
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| Added Entry
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Dietmar Ratz
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Matthias Hocks
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Rolf Hammer
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Ulrich Kulisch
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