C++ Toolbox for Verified Computing I

This book 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 (SSCM Vol. 21). The sources of the programs in this book are freely available via anonymous ftp.

Klappentext

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 reliability, analytical mathematics and verification techniques, algorithms, and (most importantly) actual C++ implementations. In each chapter, examples, exercises, and numerical results demonstrate the application of the routines presented.

Inhalt
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 rutil.- A.2 Module iutil.- A.3 Module ciutil.- A.4 Module mvutil.- A.5 Module mvi_util.- B Alphabetical List of Modules.- C List of Special Symbols.