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A Graduate Introduction to Numerical Methods

From the Viewpoint of Backward Error Analysis

  • Robert M. Corless
  • Nicolas Fillion

Table of contents

  1. Front Matter
    Pages i-xxxix
  2. Preliminaries

    1. Front Matter
      Pages 1-5
    2. Robert M. Corless, Nicolas Fillion
      Pages 7-41
    3. Robert M. Corless, Nicolas Fillion
      Pages 43-104
    4. Robert M. Corless, Nicolas Fillion
      Pages 105-162
  3. Numerical Linear Algebra

    1. Front Matter
      Pages 163-165
    2. Robert M. Corless, Nicolas Fillion
      Pages 167-237
    3. Robert M. Corless, Nicolas Fillion
      Pages 239-268
    4. Robert M. Corless, Nicolas Fillion
      Pages 269-305
    5. Robert M. Corless, Nicolas Fillion
      Pages 307-325
  4. Interpolation, Differentiation, and Quadrature

    1. Front Matter
      Pages 327-330
    2. Robert M. Corless, Nicolas Fillion
      Pages 331-401
    3. Robert M. Corless, Nicolas Fillion
      Pages 403-418
    4. Robert M. Corless, Nicolas Fillion
      Pages 419-462
    5. Robert M. Corless, Nicolas Fillion
      Pages 463-503
  5. Differential Equations

    1. Front Matter
      Pages 505-508
    2. Robert M. Corless, Nicolas Fillion
      Pages 509-583
    3. Robert M. Corless, Nicolas Fillion
      Pages 585-693
    4. Robert M. Corless, Nicolas Fillion
      Pages 695-727
    5. Robert M. Corless, Nicolas Fillion
      Pages 729-753
    6. Robert M. Corless, Nicolas Fillion
      Pages 755-791
  6. Back Matter
    Pages 793-869

About this book

Introduction

This book provides an extensive introduction to numerical computing from the viewpoint of backward error analysis. The intended audience includes students and researchers in science, engineering and mathematics. The approach taken is somewhat informal owing to the wide variety of backgrounds of the readers, but the central ideas of backward error and sensitivity (conditioning) are systematically emphasized. The book is divided into four parts: Part I provides the background preliminaries including floating-point arithmetic, polynomials and computer evaluation of functions; Part II covers numerical linear algebra; Part III covers interpolation, the FFT and quadrature; and Part IV covers numerical solutions of differential equations including initial-value problems, boundary-value problems, delay differential equations and a brief chapter on partial differential equations.

The book contains detailed illustrations, chapter summaries and a variety of exercises as well as some Matlab codes provided online as supplementary material.

 

“I really like the focus on backward error analysis and condition. This is novel in a textbook and a practical approach that will bring welcome attention." Lawrence F. Shampine

Keywords

Algorithms Backward Error Analysis Barycentric interpolation formulae Boundary Value Problems Condition number Numerical Stability

Authors and affiliations

  • Robert M. Corless
    • 1
  • Nicolas Fillion
    • 2
  1. 1.Applied MathematicsUniversity of Western OntarioLondonCanada
  2. 2.Department of PhilosophySimon Fraser UniversityBurnabyCanada

Bibliographic information