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Approximate Commutative Algebra

  • Book
  • © 2010

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Editors:
  1. Lorenzo Robbiano

    1. Dipto. Matematica, Università Genova, Genova, Italy

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  2. John Abbott

    1. Dipto. Matematica, Università Genova, Genova, Italy

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Texts & Monographs in Symbolic Computation (TEXTSMONOGR)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xiii
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  2. From Oil Fields to Hilbert Schemes

    • Martin Kreuzer, Hennie Poulisse, Lorenzo Robbiano
    Pages 1-54

  3. Numerical Decomposition of the Rank-Deficiency Set of a Matrix of Multivariate Polynomials

    • Daniel J. Bates, Jonathan D. Hauenstein, Chris Peterson, Andrew J. Sommese
    Pages 55-77

  4. Towards Geometric Completion of Differential Systems by Points

    • Wenyuan Wu, Greg Reid, Oleg Golubitsky
    Pages 79-97

  5. Geometric Involutive Bases and Applications to Approximate Commutative Algebra

    • Robin Scott, Greg Reid, Wenyuan Wu, Lihong Zhi
    Pages 99-124

  6. Regularization and Matrix Computation in Numerical Polynomial Algebra

    • Zhonggang Zeng
    Pages 125-162

  7. Ideal Interpolation: Translations to and from Algebraic Geometry

    • Boris Shekhtman
    Pages 163-192

  8. An Introduction to Regression and Errors in Variables from an Algebraic Viewpoint

    • Eva Riccomagno, Henry P. Wynn
    Pages 193-203

  9. ApCoA = Embedding Commutative Algebra into Analysis

    • Hans J. Stetter
    Pages 205-217

  10. Exact Certification in Global Polynomial Optimization Via Rationalizing Sums-Of-Squares

    • Erich Kaltofen
    Pages 219-227
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Keywords

About this book

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.

Editors and Affiliations

  • Dipto. Matematica, Università Genova, Genova, Italy

    Lorenzo Robbiano, John Abbott

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