Numerical Polynomial Algebra

Häftad, Engelska, 2004

1 525 kr

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Beskrivning

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, 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.

Produktinformation

Utgivningsdatum:2004-05-31
Mått:152 x 229 x 23 mm
Vikt:870 g
Format:Häftad
Språk:Engelska
Antal sidor:487
Förlag:Society for Industrial & Applied Mathematics,U.S.
ISBN:9780898715576

Utforska kategorier

Algebra inom Naturvetenskap och teknik

Mer om författaren

Hans J. Stetter is Professor Emeritus of Numerical Mathematics at the Vienna University of Technology, Austria. He is the author of more than 90 publications and has been editor or associate editor of Computing, Numerische Mathematik, Transactions on Numerical Software, Mathematics of Computation, and various other journals. He is a member of the German Academy of Natural Scientists Leopoldina.

Recensioner i media

'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

Innehållsförteckning

PrefacePart I: Polynomials and Numerical AnalysisChapter 1: PolynomialsChapter 2: Representations of Polynomial IdealsChapter 3: Polynomials with Coefficients of Limited AccuracyChapter 4: Approximate Numerical ComputationPart II: Univariate Polynomial ProblemsChapter 5: Univariate PolynomialsChapter 6: Various Tasks with Empirical Univariate PolynomialsPart III: Multivariate Polynomial ProblemsChapter 7: One Multivariate PolynomialChapter 8: Zero-Dimensional Systems of Multivariate PolynomialsChapter 9: Systems of Empirical Multivariate PolynomialsChapter 10: Numerical Basis ComputationPart IV: Positive-Dimensional Polynomial SystemsChapter 11: Matrix Eigenproblems for Positive-Dimensional SystemsIndex