Spline Functions Basic Theory [Paperback]

A reference/advanced text on part of applied analysis with applications in numerical analysis and computer-aided geometric design.The latest edition of this classic work continues to offer a comprehensive treatment of the theory of univariate and tensor-product splines. It includes a supplement outlining the major advances in the theory since 1981, and some 250 new references. Ideal for courses in splines, approximation theory or numerical analysis.The latest edition of this classic work continues to offer a comprehensive treatment of the theory of univariate and tensor-product splines. It includes a supplement outlining the major advances in the theory since 1981, and some 250 new references. Ideal for courses in splines, approximation theory or numerical analysis.This classic work continues to offer a comprehensive treatment of the theory of univariate and tensor-product splines. It will be of interest to researchers and students working in applied analysis, numerical analysis, computer science, and engineering. The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the biosciences. This new edition includes a supplement outlining some of the major advances in the theory since 1981, and some 250 new references. It can be used as the main or supplementary text for courses in splines, approximation theory or numerical analysis.1. Introduction; 2. Preliminaries; 3. Polynomials; 4. Polynomial splines; 5. Computational methods; 6. Approximation power of splines; 7. Approximation power of splines (free knots); 8. Other spaces of polynomial splines; 9. Tchebycheffian splines; 10. L-Splines; 11. Generalized splines; 12. Tensor-product splines; 13. Some multidimensional tools; Supplement; References; lÅ