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Scientific Computing

Vol. I - Linear and Nonlinear Equations

  • John A.┬áTrangenstein

Part of the Texts in Computational Science and Engineering book series (TCSE, volume 18)

Table of contents

  1. Front Matter
    Pages i-xxvi
  2. John A. Trangenstein
    Pages 1-27
  3. John A. Trangenstein
    Pages 29-121
  4. John A. Trangenstein
    Pages 123-289
  5. John A. Trangenstein
    Pages 291-327
  6. John A. Trangenstein
    Pages 329-427
  7. John A. Trangenstein
    Pages 429-591
  8. Back Matter
    Pages 593-622

About this book

Introduction

This is the first of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses basic principles of computation, and fundamental numerical algorithms that will serve as basic tools for the subsequent two volumes. This book and its companions show how to determine the quality of computational results, and how to measure the relative efficiency of competing methods. Readers learn how to determine the maximum attainable accuracy of algorithms, and how to select the best method for computing problems. This book also discusses programming in several languages, including C++, Fortran and MATLAB. There are 80 examples, 324 exercises, 77 algorithms, 35 interactive JavaScript programs, 391 references to software programs and 4 case studies.

Topics are introduced with goals, literature references and links to public software. There are descriptions of the current algorithms in LAPACK, GSLIB and MATLAB.

This book could be used for an introductory course in numerical methods, for either upper level undergraduates or first year graduate students.

Parts of the text could be used for specialized courses, such as principles of computer languages or numerical linear algebra.

Keywords

algorithm approximation convergence efficiency error factorization integration matrix optimization programming

Authors and affiliations

  • John A.┬áTrangenstein
    • 1
  1. 1.Professor Emeritus of Mathematics, Department of MathematicsDuke UniversityDurhamUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-69105-3
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-69104-6
  • Online ISBN 978-3-319-69105-3
  • Series Print ISSN 1611-0994
  • Series Online ISSN 2197-179X
  • Buy this book on publisher's site