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H.J. Stetter:
"Numerical Polynomial Algebra";
SIAM, Philadelphia PA, 2004, ISBN: 0-89871-557-1; 472 S.

In many important areas of scientific computing, polynomials in one or more variables are employed in the mathematical modelling of real-life phenomena, yet most of the 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 beween classical numerical analysis and classical computer algebra.

The author introduces a conceptual framework that permits the meaningful solution of various algebraic problems with multivariate polynomials 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 readers with expertise in only one of these areas.

Graduate students or academic and industrial research scientists in numerical analysis and computer algebra can use Numerical Polynomial Algebra as a textbook or reference. The book is clearly written, and standard numerical linear algebra notation is used consistently throughout. Principles and their application are explained through numerical examples and exercises avoiding excessive technical detail. Numerous open-ended problems invite further investigation and research.