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Über dieses Buch

This manual describes a PASCAL extension for scientific computation with the short title PASCAL-XSC (PASCAL eXtension for Scientific Computation). The language is the result of a long term effort of members of the Institute for Applied Mathematics of Karlsruhe University and several associated scientists. PASCAL­ XSC is intended to make the computer more powerful arithmetically than usual. It makes the computer look like a vector processor to the programmer by providing the vector/matrix operations in a natural form with array data types and the usual operator symbols. Programming of algorithms is thus brought considerably closer to the usual mathematical notation. As an additional feature in PASCAL-XSC, all predefined operators for real and complex numbers and intervals, vectors, matrices, and so on, deliver an answer that differs from the exact result by at most one rounding. Numerical mathematics has devised algorithms that deliver highly accurate and automatically verified results by applying mathematical fixed point theorems. That is, these computations carry their own accuracy control. However, their imple­ mentation requires arithmetic and programming tools that have not been available previously. The development of PASCAL-XSC has been aimed at providing these tools within the PASCAL setting. Work on the subject began during the 1960's with the development of a general theory of computer arithmetic. At first, new algorithms for the realization of the arithmetic operations had to be developed and implemented.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
This book describes the language PASCAL-XSC. The core of the language description consists of three chapters: language description, arithmetic modules, and exercises.
Ulrich Kulisch, Rudi Klatte, Dietmar Ratz, Michael Neaga, Christian Ullrich

Chapter 2. Language Reference

Abstract
PASCAL-XSC is based on the programming language PASCAL defined in the report of Jensen and Wirth [13]. Since PASCAL-XSC is an extension of PASCAL, we do not give a detailed description of the complete language (for this purpose see [9], [13], or [14] for example). Instead, we give a concise description of the standard elements of PASCAL and a rather more detailed introduction into the additional language elements of PASCAL-XSC.
Ulrich Kulisch, Rudi Klatte, Dietmar Ratz, Michael Neaga, Christian Ullrich

Chapter 3. The Arithmetic Modules

Abstract
Numerical methods require computations not only in the space of real numbers, but also with complex numbers, and vectors and matrices over these numbers (see [1], [2], [19], or [33]). To fulfill all these requirements, PASCAl-XSC provides the corresponding types with the necessary operators and functions.
Ulrich Kulisch, Rudi Klatte, Dietmar Ratz, Michael Neaga, Christian Ullrich

Chapter 4. Problem-Solving Routines

Abstract
Routines for solving common numerical problems have been developed in PASCAL-XSC. They are supplied by means of an additional module library. The methods used compute a highly accurate inclusion of the true solution of the problem and verify the existence and uniqueness of the solution in the given interval. The advantages of these new routines are:
  • The solution is computed with high accuracy, even for many ill-conditioned cases.
  • The accuracy of the computed solution is always controlled.
  • The correctness of the result is automatically verified, i.e. an inclusion set is computed which guarantees the existence and uniqueness of the exact solution within the bounds computed.
  • If no solution exists, or if the problem is extremely ill-conditioned, an error message is returned.
Ulrich Kulisch, Rudi Klatte, Dietmar Ratz, Michael Neaga, Christian Ullrich

Chapter 5. Exercises with Solutions

Abstract
Here are some exercises with which the reader can practice the language PASCAL-XSC by solving various exercises and applying the new language elements to the development of complete programs.
Ulrich Kulisch, Rudi Klatte, Dietmar Ratz, Michael Neaga, Christian Ullrich

Backmatter

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