Numerical Toolbox for Verified Computing I: Basic Numerical Problems : Theory, Algorithms, and Pascal-Xsc Programs

Description

Numerical Toolbox for Verified Computing presents an extensive set of sophisticated tools to solve basic 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. 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. This book is intended primarily as a reference text for anyone wishing to apply, modify, or develop routines to obtain mathematically certain and reliable results. It can also be used as a textbook for an advanced course in scientific computation with automatic result verification.

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