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Numerical Polynomial Algebra

Numerical Polynomial Algebra

  • Date Published: May 2004
  • 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: 9780898715576

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  • In many important areas of scientific computing, polynomials in one or more variables are employed in the mathematical modeling of real-life phenomena; yet most of classical computer algebra assumes exact rational data. This book is the first comprehensive treatment of numerical polynomial algebra, an emerging area that falls between classical numerical analysis and classical computer algebra, and which has received surprisingly little attention so far. The author introduces a conceptual framework that permits the meaningful solution of various algebraic problems with multivariate polynomial equations whose coefficients have some indeterminacy; for this purpose, he combines approaches of both numerical linear algebra and commutative algebra. For the application scientist, this book provides both a survey of polynomial problems in scientific computing that may be solved numerically and a guide to their numerical treatment. In addition, the book provides both introductory sections and novel extensions, making it more easily accessible.

    • Suitable as a textbook or reference book for graduate students or academic and industrial research scientists in numerical analysis and computer algebra
    • Clearly written with standard numerical linear algebra notation used consistently throughout
    • Numerical examples and exercises avoid excessive technical detail, while numerous open-ended problems invite further investigation and research
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    Reviews & endorsements

    'This first book on the numerical analysis of polynomial systems is a stepping stone at the interface of symbolic computation and numerical computation.' Bernard Sturmfels, University of Berkeley

    'I am not familiar with any books that do such a careful job of combining numerical analysis with the algebra of polynomial equations. Dr Stetter's book is unique in this regard.' David Cox, Amherst College

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    Product details

    • Date Published: May 2004
    • format: Paperback
    • isbn: 9780898715576
    • length: 184 pages
    • dimensions: 255 x 178 x 23 mm
    • weight: 0.86kg
    • 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

    Preface
    Part I. Polynomials and Numerical Analysis:
    1. Polynomials
    2. Representations of polynomial ideals
    3. Polynomials with coefficients of limited accuracy
    4. Approximate numerical computation
    Part II. Univariate Polynomial Problems:
    5. Univariate polynomials
    6. Various tasks with empirical univariate polynomials
    Part III. Multivariate Polynomial Problems:
    7. One multivariate polynomial
    8. Zero-dimensional systems of multivariate polynomials
    9. Systems of empirical multivariate polynomials
    10. Numerical basis computation
    Part IV. Positive-Dimensional Polynomial Systems:
    11. Matrix eigenproblems for positive-dimensional systems
    Index.

  • Author

    Hans J. Stetter, Technische Universität Wien, Austria

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