Approximate Commutative Algebra [electronic resource] / edited by Lorenzo Robbiano, John Abbott.

Contributor(s): Robbiano, Lorenzo [editor.] | Abbott, John [editor.] | SpringerLink (Online service)
Material type: TextTextSeries: Texts and Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria: Publisher: Vienna : Springer Vienna, 2010Description: XIV, 227 p. 15 illus., 4 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783211993149Subject(s): Mathematics | Computer science -- Mathematics | Algebraic geometry | Commutative algebra | Commutative rings | Numerical analysis | Mathematics | Algebraic Geometry | Commutative Rings and Algebras | Numerical Analysis | Symbolic and Algebraic ManipulationAdditional physical formats: Printed edition:: No titleDDC classification: 516.35 LOC classification: QA564-609Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
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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.

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.

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