Ebook: 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.

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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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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.
Content:
Front Matter....Pages i-xiii
From Oil Fields to Hilbert Schemes....Pages 1-54
Numerical Decomposition of the Rank-Deficiency Set of a Matrix of Multivariate Polynomials....Pages 55-77
Towards Geometric Completion of Differential Systems by Points....Pages 79-97
Geometric Involutive Bases and Applications to Approximate Commutative Algebra....Pages 99-124
Regularization and Matrix Computation in Numerical Polynomial Algebra....Pages 125-162
Ideal Interpolation: Translations to and from Algebraic Geometry....Pages 163-192
An Introduction to Regression and Errors in Variables from an Algebraic Viewpoint....Pages 193-203
ApCoA = Embedding Commutative Algebra into Analysis....Pages 205-217
Exact Certification in Global Polynomial Optimization Via Rationalizing Sums-Of-Squares....Pages 219-227

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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.
Content:
Front Matter....Pages i-xiii
From Oil Fields to Hilbert Schemes....Pages 1-54
Numerical Decomposition of the Rank-Deficiency Set of a Matrix of Multivariate Polynomials....Pages 55-77
Towards Geometric Completion of Differential Systems by Points....Pages 79-97
Geometric Involutive Bases and Applications to Approximate Commutative Algebra....Pages 99-124
Regularization and Matrix Computation in Numerical Polynomial Algebra....Pages 125-162
Ideal Interpolation: Translations to and from Algebraic Geometry....Pages 163-192
An Introduction to Regression and Errors in Variables from an Algebraic Viewpoint....Pages 193-203
ApCoA = Embedding Commutative Algebra into Analysis....Pages 205-217
Exact Certification in Global Polynomial Optimization Via Rationalizing Sums-Of-Squares....Pages 219-227
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