Skip to content
Register Sign in Wishlist
Lectures on Finite Precision Computations

Lectures on Finite Precision Computations

£59.00

Part of Software, Environments and Tools

  • Date Published: February 1997
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898713589

£ 59.00
Paperback

This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Unavailable Add to wishlist

Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • Devoted to the assessment of the quality of numerical results produced by computers, this book addresses the question: How does finite precision affect the convergence of numerical methods on the computer when convergence has been proven in exact arithmetic? Finite precision computations are at the heart of the daily activities of many engineers and researchers in all branches of applied mathematics. Written in an informal style, the book combines techniques from engineering and mathematics to describe the rigorous and novel theory of computability in finite precision. In the challenging cases of nonlinear problems, theoretical analysis is supplemented by software tools to explore the stability on the computer. Roundoff errors are often considered negatively, as a severe limitation on the purity of exact computations. The authors show how the necessarily finite precision of the computer arithmetic can be turned into an asset to describe physical phenomena.

    Reviews & endorsements

    'Chaitin-Chatelin and Frayssé provide a rigorous basis for error analysis and asses the quality and reliability of computations. ... Problems and algorithm derivations, toolboxes for computer experimentation, are given in a clear succinct form.' D. E. Bentil, CHOICE

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: February 1997
    • format: Paperback
    • isbn: 9780898713589
    • length: 250 pages
    • dimensions: 253 x 179 x 15 mm
    • weight: 0.452kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    Foreword Iain S. Duff
    Preface
    General Presentation Notations. Part I. Computability in Finite Precision: Well-Posed Problems
    Approximations
    Convergence in Exact Arithmetic
    Computability in Finite Precision
    Gaussian Elimination
    Forward Error Analysis
    The Influence of Singularities
    Numerical Stability in Exact Arithmetic
    Computability in Finite Precision for Iterative and Approximate Methods
    The Limit of Numerical Stability in Finite Precision
    Arithmetically Robust Convergence
    The Computed Logistic
    Bibliographical Comments. Part II. Measures of Stability for Regular Problems: Choice of Data and Class of Perturbations
    Choice of Norms: Scaling
    Conditioning of Regular Problems
    Simple Roots of Polynomials
    Factorizations of a Complex Matrix
    Solving Linear Systems
    Functions of a Square Matrix
    Concluding Remarks
    Bibliographical Comments. Part III. Computation in the Neighbourhood of a Singularity: Singular Problems Which are Well-Posed
    Condition Numbers of Hölder-Singularities
    Computability of Ill-Posed Problems
    Singularities of z ----> A - zI
    Distances to Singularity
    Unfolding of Singularity
    Spectral Portraits
    Bibliographical Comments. Part IV. Arithmetic Quality of Reliable Algorithms: Forward and Backward Analyses
    Backward Error
    Quality of Reliable Software
    Formulae for Backward Errors
    Influence of the Class of Perturbations
    Iterative Refinement for Backward Stability
    Robust Reliability and Arithmetic Quality
    Bibliographical Comments. Part V. Numerical Stability in Finite Precision: Iterative and Approximate Methods
    Numerical Convergence of Iterative Solvers
    Stopping Criteria in Finite Precision
    Robust Convergence
    The Computed Logistic Revisited
    Care of Use
    Bibliographical Comments. PartVI. Software Tools for Round-Off Error Analysis in Algorithms. A Historical Perspective
    The Assessment of the Quality of the Numerical Software
    Backward Error Analysis in Libraries
    Sensitivity Analysis
    Interval Analysis
    Probabilisitc Models
    Computer Algebra
    Bibliographical Comments. Part VII. The Toolbox PRECISE for Computer Experimentation. What is PRECISE?
    Module for Backward Error Analysis
    Sample Size
    Backward Analysis with PRECISE
    Dangerous Border and Unfolding of a Singularity
    Summary of Module 1
    Bibliographical Comments. Part VIII. Experiments with PRECISE. Format of the Examples
    Backward Error Analysis for Linear Systems
    Computer Unfolding of Singularity
    Dangerous Border and Distance to Singularity
    Roots of Polynomials
    Eigenvalue Problems
    Conclusion
    Bibliographical Comments. Part IX. Robustness to Nonnormality. Nonnormality and Spectral Instability
    Nonnormality in Physics and Technology
    Convergence of Numerical Methods in Exact Arithmetic
    Influence on Numerical Software
    Bibliographical Comments. Part V. Qualitative Computing. Sensitivity and Pseudosolutions for F (x) = y: Pseudospectra of Matrices
    Pseudozeroes of Polynomials
    Divergence Portrait for the Complex Logistic Iteration
    Qualitative Computation of a Jordan Form
    Beyond Linear Perturbation Theory
    Bibliographical Comments. Part XI. More Numerical Illustrations with PRECISE: Annex: The Toolbox PRECISE for MATLAB
    Index
    Bibliography.

  • Authors

    Françoise Chaitin-Chatelin, Université de Toulouse I (Sciences Sociales)

    Valérie Frayssé, CERFACS, Toulouse

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×