Solving Polynomial Equations | Taschenbuch

Cover: 9783642063619 | Solving Polynomial Equations | Ioannis Z. Emiris (u. a.) | Taschenbuch

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Beschreibung

The subject of this book is the solution of polynomial equations, that is, s- tems of (generally) non-linear algebraic equations. This study is at the heart of several areas of mathematics and its applications. It has provided the - tivation for advances in di?erent branches of mathematics such as algebra, geometry, topology, and numerical analysis. In recent years, an explosive - velopment of algorithms and software has made it possible to solve many problems which had been intractable up to then and greatly expanded the areas of applications to include robotics, machine vision, signal processing, structural molecular biology, computer-aided design and geometric modelling, as well as certain areas of statistics, optimization and game theory, and b- logical networks. At the same time, symbolic computation has proved to be an invaluable tool for experimentation and conjecture in pure mathematics. As a consequence, the interest in e?ective algebraic geometry and computer algebrahasextendedwellbeyonditsoriginalconstituencyofpureandapplied mathematicians and computer scientists, to encompass many other scientists and engineers. While the core of the subject remains algebraic geometry, it also calls upon many other aspects of mathematics and theoretical computer science, ranging from numerical methods, di?erential equations and number theory to discrete geometry, combinatorics and complexity theory. Thegoalofthisbookistoprovideageneralintroduction tomodernma- ematical aspects in computing with multivariate polynomials and in solving algebraic systems.

Zusammenfassung

This useful collection provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the state of the art in several symbolic, numeric, and symbolic-numeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and a range of applications. Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics.

Inhaltsverzeichnis

to residues and resultants.- Solving equations via algebras.- Symbolic-numeric methods for solving polynomial equations and applications.- An algebraist¿s view on border bases.- Tools for computing primary decompositions and applications to ideals associated to Bayesian networks.- Algorithms and their complexities.- Toric resultants and applications to geometric modelling.- to numerical algebraic geometry.- Four lectures on polynomial absolute factorization.

Erscheinungsjahr:	2010
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Algorithms and Computation in Mathematics
Inhalt:	xiv 426 S. 33 s/w Illustr. 11 farbige Illustr. 426 p. 44 illus. 11 illus. in color.
ISBN-13:	9783642063619
ISBN-10:	3642063616
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Redaktion:	Emiris, Ioannis Z. Dickenstein, Alicia
Herausgeber:	Alicia Dickenstein/Ioannis Z Emiris
Auflage:	Softcover reprint of hardcover 1st ed. 2005
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg Algorithms and Computation in Mathematics
Maße:	235 x 155 x 24 mm
Von/Mit:	Ioannis Z. Emiris (u. a.)
Erscheinungsdatum:	21.10.2010
Gewicht:	0,663 kg

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