Approximate Commutative Algebra

• Corporate Author: SpringerLink (Online service)
• Other Authors: Robbiano, Lorenzo. (Editor), Abbott, John. (Editor)
• Format: Electronic
• Language: English
• Published: Vienna : Springer Vienna, 2010.
• Series: Texts and Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria,
• Subjects: Mathematics.; Algebra > Data processing.; Geometry, algebraic.; Algebra.; Numerical analysis.; Algebraic Geometry.; Commutative Rings and Algebras.; Numerical Analysis.; Symbolic and Algebraic Manipulation.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-211-99314-9

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...

Table 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.