Approximate Commutative Algebra

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

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.

• algebra
• algebraic geometry
• approximate commutative algebra
• calculus
• commutative algebra
• computation
• geometry

• Dipto. Matematica, Università Genova, Genova, Italy

  Lorenzo Robbiano, John Abbott

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