A thorough introduction to the theory that is the basis of current approximation methods with emphasis on piecewise polynomials.
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.
Review
"Of its kind, this book is excellent, perhaps the best." Journal of Classification
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