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Numerical Polynomial Algebra <br />
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Type.................: Ebook<br />
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Posted by............: ~tqw~<br />
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Release Notes<br />
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In many important areas of scientific computing, polynomials in one or more <br />
variables are employed in the mathematical modeling of real-life phenomena; yet <br />
most of classical computer algebra assumes exact rational data. This book is the <br />
first comprehensive treatment of the emerging area of numerical polynomial <br />
algebra, an area that falls between classical numerical analysis and classical <br />
computer algebra but, surprisingly, has received little attention so far.<br />
<br />
The author introduces a conceptual framework that permits the meaningful <br />
solution of various algebraic problems with multivariate polynomial equations <br />
whose coefficients have some indeterminacy; for this purpose, he combines <br />
approaches of both numerical linear algebra and commutative algebra. For the <br />
application scientist, Numerical Polynomial Algebra provides both a survey of <br />
polynomial problems in scientific computing that may be solved numerically and a <br />
guide to their numerical treatment. In addition, the book provides both <br />
introductory sections and novel extensions of numerical analysis and computer <br />
algebra, making it accessible to the reader with expertise in either one of <br />
these areas.<br />
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Table of Contents<br />
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Preface<br />
Part I: Polynomials and Numerical Analysis<br />
Chapter 1: Polynomials<br />
Chapter 2: Representations of Polynomial Ideals<br />
Chapter 3: Polynomials with Coefficients of Limited Accuracy<br />
Chapter 4: Approximate Numerical Computation<br />
Part II: Univariate Polynomial Problems<br />
Chapter 5: Univariate Polynomials<br />
Chapter 6: Various Tasks with Empirical Univariate Polynomials<br />
Part III: Multivariate Polynomial Problems<br />
Chapter 7: One Multivariate Polynomial<br />
Chapter 8: Zero-Dimensional Systems of Multivariate Polynomials<br />
Chapter 9: Systems of Empirical Multivariate Polynomials<br />
Chapter 10: Numerical Basis Computation<br />
Part IV: Positive-Dimensional Polynomial Systems<br />
Chapter 11: Matrix Eigenproblems for Positive-Dimensional Systems<br />
Index<br />
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Product Details<br />
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* ISBN: 0898715571<br />
* ISBN-13: 9780898715576<br />
* Format: Paperback, 472pp<br />
* Publisher: SIAM<br />
* Pub. Date: January 2004<br />
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