# A Course in Approximation Theory

### About this Title

**Ward Cheney**, *University of Texas at Austin, Austin, TX* and **Will Light**

Publication: Graduate Studies in Mathematics

Publication Year
2009: Volume 101

ISBNs: 978-0-8218-4798-5 (print); 978-1-4704-1165-7 (online)

DOI: http://dx.doi.org/10.1090/gsm/101

MathSciNet review: MR2474372

MSC: Primary 41-01

### Table of Contents

**Front/Back Matter**

**Chapters**

- Chapter 1. Introductory discussion of interpolation
- Chapter 2. Linear interpolation operators
- Chapter 3. Optimization of the Lagrange operator
- Chapter 4. Multivariate polynomials
- Chapter 5. Moving the nodes
- Chapter 6. Projections
- Chapter 7. Tensor-product interpolation
- Chapter 8. The Boolean algebra of projections
- Chapter 9. The Newton paradigm for interpolation
- Chapter 10. The Lagrange paradigm for interpolation
- Chapter 11. Interpolation by translates of a single function
- Chapter 12. Positive definite functions
- Chapter 13. Strictly positive definite functions
- Chapter 14. Completely monotone functions
- Chapter 15. The Schoenberg interpolation theorem
- Chapter 16. The Micchelli interpolation theorem
- Chapter 17. Positive definite functions on spheres
- Chapter 18. Approximation by positive definite functions
- Chapter 19. Approximation reconstruction of functions and tomography
- Chapter 20. Approximation by convolution
- Chapter 21. The good kernels
- Chapter 22. Ridge functions
- Chapter 23. Ridge function approximation via convolutions
- Chapter 24. Density of ridge functions
- Chapter 25. Artificial neural networks
- Chapter 26. Chebyshev centers
- Chapter 27. Optimal reconstruction of functions
- Chapter 28. Algorithmic orthogonal projections
- Chapter 29. Cardinal B-splines and the sinc function
- Chapter 30. The Golomb-Weinberger theory
- Chapter 31. Hilbert function spaces and reproducing kernels
- Chapter 32. Spherical thin-plate splines
- Chapter 33. Box splines
- Chapter 34. Wavelets, I
- Chapter 35. Wavelets II
- Chapter 36. Quasi-interpolation