Approximate Commutative Algebra

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.

List of contents

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.

Summary

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.

Product details

• Assisted by: Abbott (Editor), Abbott (Editor), John Abbott (Editor), Lorenz Robbiano (Editor), Lorenzo Robbiano (Editor)
• Publisher: Springer, Wien
• Languages: English
• Product format: Paperback / Softback
• Released: 16.10.2009
• EAN: 9783211993132
• ISBN: 978-3-211-99313-2
• No. of pages: 227
• Dimensions: 173 mm x 11 mm x 238 mm
• Weight: 424 g
• Illustrations: XIV, 227 p. 15 illus., 4 illus. in color.
• Series: Texts & Monographs in Symbolic Computation; Texts and Monographs in Symbolic Computation; Texts & Monographs in Symbolic Computation
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, B, Mathematik für Informatiker, Mathematics and Statistics, Algebraic Geometry, Commutative algebra, Commutative rings, Commutative Rings and Algebras, Numerical analysis, Computer science—Mathematics, Maths for computer scientists, Symbolic and Algebraic Manipulation