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Numerical Polynomial Algebra
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Type.................: Ebook
Part Size............: 21,898,392 bytes




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Posted by............: ~tqw~

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Release Notes
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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 the emerging area of numerical polynomial
algebra, an area that falls between classical numerical analysis and classical
computer algebra but, surprisingly, has received 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, Numerical Polynomial Algebra 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 of numerical analysis and computer
algebra, making it accessible to the reader with expertise in either one of
these areas.

Table of Contents

Preface
Part I: Polynomials and Numerical Analysis
Chapter 1: Polynomials
Chapter 2: Representations of Polynomial Ideals
Chapter 3: Polynomials with Coefficients of Limited Accuracy
Chapter 4: Approximate Numerical Computation
Part II: Univariate Polynomial Problems
Chapter 5: Univariate Polynomials
Chapter 6: Various Tasks with Empirical Univariate Polynomials
Part III: Multivariate Polynomial Problems
Chapter 7: One Multivariate Polynomial
Chapter 8: Zero-Dimensional Systems of Multivariate Polynomials
Chapter 9: Systems of Empirical Multivariate Polynomials
Chapter 10: Numerical Basis Computation
Part IV: Positive-Dimensional Polynomial Systems
Chapter 11: Matrix Eigenproblems for Positive-Dimensional Systems
Index

Product Details

* ISBN: 0898715571
* ISBN-13: 9780898715576
* Format: Paperback, 472pp
* Publisher: SIAM
* Pub. Date: January 2004

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