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AuthorKulisch, Ulrich. author
TitleC++ Toolbox for Verified Computing I [electronic resource] : Basic Numerical Problems Theory, Algorithms, and Programs / by Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1995
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Descript XVIII, 382 p. online resource


This C++ Toolbox for Verified Computing presents an extensive set of sophisticated tools for solving basic numerical problems with verification of the results. It is the C++ edition of the Numerical Toolbox for Verified Computing which was based on the computer language PASCAL-XSC. The sources of the programs in this book are freely available via anonymous ftp. This book offers a general discussion on arithmetic and computational reliablility, analytical mathematics and verification techniques, algoriths, and (most importantly) actual C++ implementations. In each chapter, examples, exercises, and numerical results demonstrate the application of the routines presented. The book introduces many computational verification techniques. It is not assumed that the reader has any prior formal knowledge of numerical verification or any familiarity with interval analysis. The necessary concepts are introduced. Some of the subjects that the book covers in detail are not usually found in standard numerical analysis texts


1 Introduction -- 1.1 Advice for Quick Reading -- 1.2 Structure of the Book -- 1.3 Typography -- 1.4 Algorithmic Notation -- 1.5 Implementation -- 1.6 Computational Environment -- 1.7 Why Numerical Result Verification? -- I Preliminaries -- 2 The Features of C-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.1 Module r_util -- A.2 Module i_util -- A.3 Module ci_util -- A.4 Module mv_util -- A.5 Module mvi_util -- B Alphabetical List of Modules -- C List of Special Symbols

Mathematics Mathematical analysis Analysis (Mathematics) Algorithms Numerical analysis Physics Applied mathematics Engineering mathematics Mathematics Numerical Analysis Analysis Algorithms Appl.Mathematics/Computational Methods of Engineering Mathematical Methods in Physics Numerical and Computational Physics


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