Description
Springer Solving Polynomial Equations Foundations Algorithms And Applications 2005 Edition by Alicia Dickenstein Ioannis Z. Emiris
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. Table of contents : 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.