Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1Quadrature Rules and Orthogonal Polynomials
- 2Cubature Rules: Basics
- 3Orthogonal Polynomials of Several Variables
- 4Gauss Cubature Rules
- 5Lower Bounds for the Number of Nodes
- 6First Minimal Cubature Rules
- 7Further Minimal Cubature Rules
- 8Discrete Fourier Transform and Cubature Rules
- 9Cubature Rules and Polynomial Ideals
- 10Epilogue: Two Open Problems
- 11Addendum: Cubature Rules on the Triangle and Simplex
- References
- Index
3 - Orthogonal Polynomials of Several Variables
Published online by Cambridge University Press: 10 October 2025
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1Quadrature Rules and Orthogonal Polynomials
- 2Cubature Rules: Basics
- 3Orthogonal Polynomials of Several Variables
- 4Gauss Cubature Rules
- 5Lower Bounds for the Number of Nodes
- 6First Minimal Cubature Rules
- 7Further Minimal Cubature Rules
- 8Discrete Fourier Transform and Cubature Rules
- 9Cubature Rules and Polynomial Ideals
- 10Epilogue: Two Open Problems
- 11Addendum: Cubature Rules on the Triangle and Simplex
- References
- Index
Summary
Orthogonal polynomials play an important role in the study of cubature rules. Minimal cubature rules are often characterized via common zeros of orthogonal polynomials, and they are studied with the help of the structure relations of orthogonal polynomials. This chapter provides a concise and self-contained account of orthogonal polynomials in several variables.
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- Minimal Cubature RulesTheory and Practice, pp. 45 - 72Publisher: Cambridge University PressPrint publication year: 2025
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