عنوان

Numerical Toolbox for Verified Computing I :

3642784232

9783642784231

b573825

Numerical Toolbox for Verified Computing I :

[Book]

Basic Numerical Problems Theory, Algorithms, and Pascal-XSC Programs

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

Berlin, Heidelberg

Springer Berlin Heidelberg

1993

(xv, 339 pages 28 illustrations)

Springer series in computational mathematics, 21.

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.

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.

Computer science.

Mathematics.

Numerical analysis.

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

Dietmar Ratz

Matthias Hocks

Rolf Hammer

Ulrich Kulisch

[Book]

Y