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Quadrature Theory: The Theory of Numerical Integration on a Compact Interval
About this Title
Helmut Brass, Technische Universität Braunschweig, Braunschweig, Germany and Knut Petras, Technische Universität Braunschweig, Braunschweig, Germany
Publication: Mathematical Surveys and Monographs
Publication Year:
2011; Volume 178
ISBNs: 978-0-8218-5361-0 (print); 978-1-4704-1405-4 (online)
DOI: https://doi.org/10.1090/surv/178
MathSciNet review: 2840013
MSC: Primary 65D30; Secondary 41A05, 41A55
Table of Contents
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Front/Back Matter
Chapters
- 1. Introduction
- 2. The abstract framework
- 3. Norm and kernel of the remainder functional
- 4. Co-observations
- 5. Quadrature rules of interpolatory type
- 6. Gaussian quadrature
- 7. Quadrature rules with equidistant nodes
- 8. Periodic integrands
- 9. Variance and Chebyshev-type rules
- 10. Problems
- Appendix A. Orthogonal polynomials
- Appendix B. Bernoulli polynomials
- Appendix C. Validation of co-observations