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Springer Series in Computational Mathematics

Numerical Toolbox for Verified Computing I

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

Authors: Hammer, R., Hocks, M., Kulisch, U., Ratz, D.

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eBook $119.00
price for USA in USD (gross)
  • ISBN 978-3-642-78423-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
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  • Immediate eBook download after purchase
Softcover $159.00
price for USA in USD
  • ISBN 978-3-642-78425-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

As suggested by the title of this book Numerical Toolbox for Verified Computing, we present an extensive set of sophisticated tools to solve basic numerical problems with a verification of the results. We use the features of the scientific computer language PASCAL-XSC to offer modules that can be combined by the reader to his/her individual needs. Our overriding concern is reliability - the automatic verification of the result a computer returns for a given problem. All algorithms we present are influenced by this central concern. We must point out that there is no relationship between our methods of numerical result verification and the methods of program verification to prove the correctness of an imple~entation for a given algorithm. 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. Our task has been to find the right balance among these ingredients for each topic. For some topics, we have placed a little more emphasis on the algorithms. For other topics, where the mathematical prerequisites are universally held, we have tended towards more in-depth discussion of the nature of the computational algorithms, or towards practical questions of implementation. For all topics, we present exam­ ples, exercises, and numerical results demonstrating the application of the routines presented.

Table of contents (14 chapters)

  • Introduction

    Kulisch, Prof.Dr. Ulrich (et al.)

    Pages 1-14

  • The Features of PASCAL-XSC

    Kulisch, Prof.Dr. Ulrich (et al.)

    Pages 17-30

  • Mathematical Preliminaries

    Kulisch, Prof.Dr. Ulrich (et al.)

    Pages 31-53

  • Evaluation of Polynomials

    Kulisch, Prof.Dr. Ulrich (et al.)

    Pages 57-68

  • Automatic Differentiation

    Kulisch, Prof.Dr. Ulrich (et al.)

    Pages 69-86

Buy this book

eBook $119.00
price for USA in USD (gross)
  • ISBN 978-3-642-78423-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $159.00
price for USA in USD
  • ISBN 978-3-642-78425-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Numerical Toolbox for Verified Computing I
Book Subtitle
Basic Numerical Problems Theory, Algorithms, and Pascal-XSC Programs
Authors
Series Title
Springer Series in Computational Mathematics
Series Volume
21
Copyright
1993
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-78423-1
DOI
10.1007/978-3-642-78423-1
Softcover ISBN
978-3-642-78425-5
Series ISSN
0179-3632
Edition Number
1
Number of Pages
XV, 339
Topics