عنوان

C++ Toolbox for Verified Computing I :

3642796516

3642796532

9783642796517

9783642796531

b574003

C++ Toolbox for Verified Computing I :

[Book]

Basic Numerical Problems Theory, Algorithms, and Programs

by Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz.

Berlin, Heidelberg

Springer Berlin Heidelberg

1995

(XVIII, 382 pages)

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.

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.

Theory, Algorithms, and Programs

Algorithms.

Global analysis (Mathematics)

Mathematics.

by Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz.

Dietmar Ratz

Matthias Hocks

Rolf Hammer

Ulrich Kulisch

[Book]

Y