Solving Polynomial Equations

Foundations, Algorithms, and Applications

AvAlicia Dickenstein,Ioannis Z. Emiris

Inbunden, Engelska, 2005

Del 14 i serien Algorithms and Computation in Mathematics

538 kr

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Beskrivning

This book 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 applications ranging from statistics and geometric modelling to robotics and vision.Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants, residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications.

Produktinformation

Utgivningsdatum:2005-04-27
Mått:155 x 235 x 32 mm
Vikt:910 g
Format:Inbunden
Språk:Engelska
Serie:Algorithms and Computation in Mathematics
Antal sidor:426
Upplaga:2005
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540243267

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Recensioner i media

From the reviews of the first edition: "[...] The editors of the book - Alicia Dickenstein and Ioannis Emiris - have done a very good job in collecting a set of expository lectures on a very interesting branch of mathematics. I imagine that this book will be of use to anyone working in the area, and would be a good introduction for a graduate student or someone wishing to start working in the field. [...]" Darren Glass, MAA Review, January 2006 "Dieses Buch besteht aus neun weitgehend unabhangigen Kapiteln zum Thema "Losung polynomialer Gleichungssysteme", geschrieben von bekannten Experten. Der Schwerpunkt liegt auf spezialisierten Themen, bei denen in jungerer Zeit beachtliche Fortschritte erzielt wurden. Es gibt deshalb wenig Uberschneidungen mit anderen Buchern der Computeralgebra. [...] Insgesamt ist dieses Buch eine reiche Quelle von Informationen und eine sehr willkommene Erganzung zu den bereits vorhandenen Lehrbuchern im Bereich der Losung polynomialer Gleichungssysteme. Es sollte in keinem Regal fehlen." Peter Burgisser, Computeralgebra, Ausgabe 39, Oktober 2006 "Although about 15 authors have contributed to this book it constitutes a unified whole. Its subjects are the diverse methods, techniques and algorithms in solving multivariate (non-linear) polynomial equations or systems of them, which mostly have been developed in recent years. ... All in all there is presented a detailed account, which often leads to the front of research." (G. Kowol, Monatshefte fur Mathematik, Vol. 148 (4), 2006)

Innehållsförteckning

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.