Numerical Polynomial Algebra

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SIAM, May 1, 2004 - Mathematics - 472 pages
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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.
  

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Contents

Polynomials
3
Representations of Polynomial Ideals
25
Polynomials with Coefficients of Limited Accuracy
67
Approximate Numerical Computation
101
Univariate Polynomials
135
Various Tasks with Empirical Univariate Polynomials
173
One Multivariate Polynomial
229
Zero Dimensional Systems of Multivariate Polynomials
273
Systems of Empirical Multivariate Polynomials
343
Numerical Basis Computation
411
Matrix Eigenproblems for PositiveDimensional Systems
447
Index
467
Copyright

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About the author (2004)

Stetter is Professor Emeritus of Numerical Mathematics at the Vienna University of Technology, Austria. He is a member of the German Academy of Natural Scientists Leopoldina.

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