A Graduate Introduction to Numerical Methods

From the Viewpoint of Backward Error Analysis

Authors: Corless, Robert, Fillion, Nicolas

  • ​Provides consistent development of formulae using barycentric interpolation
  • Independence of chapters allowing for greater teaching flexibility
  • Integration with Matlab and Maple, many algorithms presented in pseudocode
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  • ISBN 978-1-4614-8453-0
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Hardcover $99.00
price for USA
  • ISBN 978-1-4614-8452-3
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Softcover $99.00
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About this Textbook

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 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

A Graduate Introduction to Numerical Methods and Backward Error Analysis” has been selected by Computing Reviews as a notable book in computing in 2013.  Computing Reviews Best of 2013 list consists of book and article nominations from reviewers, CR category editors, the editors-in-chief of journals, and others in the computing community.

 

About the authors

“A Graduate Introduction to Numerical Methods and Backward Error Analysis” has been selected as a notable book in computing in 2013.  Computing Reviews’ Best of 2013 list consists of book and article nominations from reviewers, CR category editors, the editors-in-chief of journals, and others in the computing community.

Reviews

“Corless and Fillion have clearly dedicated several years of their lives to this book. It has been worth it! The result is a carefully judged all-round numerical analysis textbook that expertly serves students and instructors. The book stands out in a crowded market. It is a textbook that numerical analysis can be very proud of.” (Alex Townsend, SIAM Review, Vol. 58 (4), December, 2016)

“This book is intended to be a graduate introduction to numerical methods from the perspective of backward error analysis. … it is the variety of topics and case studies, both theoretical and numerical, presented in the book that is its strongest point, making it a valuable reference work for students and professionals … .” (Justin Steven C. Prentice, Mathematical Reviews, January, 2015)

“This textbook provides a very readable and comprehensive graduate-level introduction to numerical methods and their analysis. … The textbook contains many references, exercises, MATLAB codes, and numerical illustrations. It is written in a style that is both informal and informative which makes this book unique in fact.” (Robert Plato, zbMATH, Vol. 1295, 2014)

Table of contents (16 chapters)

  • Computer Arithmetic and Fundamental Concepts of Computation

    Corless, Robert M. (et al.)

    Pages 7-41

  • Polynomials and Series

    Corless, Robert M. (et al.)

    Pages 43-104

  • Rootfinding and Function Evaluation

    Corless, Robert M. (et al.)

    Pages 105-162

  • Solving Ax=b

    Corless, Robert M. (et al.)

    Pages 167-237

  • Solving Ax = λx

    Corless, Robert M. (et al.)

    Pages 239-268

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4614-8453-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-1-4614-8452-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
price for USA
  • ISBN 978-1-4939-5310-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
A Graduate Introduction to Numerical Methods
Book Subtitle
From the Viewpoint of Backward Error Analysis
Authors
Copyright
2014
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
Distribution Rights
Distribution rights for India: Delhi Book Store, New Delhi, India
eBook ISBN
978-1-4614-8453-0
DOI
10.1007/978-1-4614-8453-0
Hardcover ISBN
978-1-4614-8452-3
Softcover ISBN
978-1-4939-5310-3
Edition Number
1
Number of Pages
XXXIX, 869
Number of Illustrations and Tables
184 b/w illustrations, 10 illustrations in colour
Topics