Synopses & Reviews
'A thorough introduction to the theory that is the basis of current approximation methods with emphasis on piecewise polynomials.'
Review
"Of its kind, this book is excellent, perhaps the best." Journal of Classification
Table of Contents
Preface; 1. The approximation problem and existence of best approximations; 2. The uniqueness of best approximations; 3. Approximation operators and some approximating functions; 4. Polynomial interpolation; 5. Divided differences; 6. The uniform convergence of polynomial approximations; 7. The theory of minimax approximation; 8. The exchange algorithm; 9. The convergence of the exchange algorithm; 10. Rational approximation by the exchange algorithm; 11. Least squares approximation; 12. Properties of orthogonal polynomials; 13. Approximation of periodic functions; 14. The theory of best L1 approximation; 15. An example of L1 approximation and the discrete case; 16. The order of convergence of polynomial approximations; 17. The uniform boundedness theorem; 18. Interpolation by piecewise polynomials; 19. B-splines; 20. Convergence properties of spline approximations; 21. Knot positions and the calculation of spline approximations; 22. The Peano kernel theorem; 23. Natural and perfect splines; 24. Optimal interpolation; Appendices; Index.