Approximate Commutative Algebra

2010
ISBN: 978-3-211-99313-2
Verlag: Springer Vienna

Buch, Englisch, 227 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 421 g

Reihe: Texts & Monographs in Symbolic Computation

Approximate Commutative Algebra is an emerging field of research which endeavours to bridge the gap between traditional exact Computational Commutative Algebra and approximate numerical computation. The last 50 years have seen enormous progress in the realm of exact Computational Commutative Algebra, and given the importance of polynomials in scientific modelling, it is very natural to want to extend these ideas to handle approximate, empirical data deriving from physical measurements of phenomena in the real world. In this volume nine contributions from established researchers describe various approaches to tackling a variety of problems arising in Approximate Commutative Algebra.

Zielgruppe

Research

Autoren/Hrsg.

Abbott, John

Robbiano, Lorenzo

Weitere Mitwirkende

Robbiano, Lorenzo

Abbott, John

Fachgebiete

• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Algebra Elementare Algebra
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis

Inhaltsverzeichnis

From Oil Fields to Hilbert Schemes.- Numerical Decomposition of the Rank-Deficiency Set of a Matrix of Multivariate Polynomials.- Towards Geometric Completion of Differential Systems by Points.- Geometric Involutive Bases and Applications to Approximate Commutative Algebra.- Regularization and Matrix Computation in Numerical Polynomial Algebra.- Ideal Interpolation: Translations to and from Algebraic Geometry.- An Introduction to Regression and Errors in Variables from an Algebraic Viewpoint.- ApCoA = Embedding Commutative Algebra into Analysis.- Exact Certification in Global Polynomial Optimization Via Rationalizing Sums-Of-Squares.