Spline Functions: Computational Methods

Spline Functions: Computational Methods

This book describes in detail the key algorithms needed for computing with spline functions and illustrates their use in solving several basic problems in numerical analysis, including function approximation, numerical quadrature, data fitting, and the numerical solution of PDEs. The focus is on computational methods for bivariate splines on triangulations in the plane and on the sphere, although both univariate and tensor-product splines are also discussed.<p> <p> The book contains numerous examples and figures to illustrate the methods and their performance. All of the algorithms in the book have been coded in a separate MATLAB package available for license. The package can be used to run all of the examples in the book and also provides readers with the essential tools needed to create software for their own applications. In addition to the included bibliography, a list of over 100 pages of additional references can be found on the book's website.<p> <p> <b>Audience:</b> This book is designed for mathematicians, engineers, scientists, and anyone else wanting to make use of spline functions for numerical computation.<p> <p> <b>Contents:</b> Preface; Chapter 1: Univariate Splines; Chapter 2: Tensor-Product Splines; Chapter 3: Computing with Triangulations; Chapter 4: Computing with Splines; Chapter 5: Macro-element Interpolation Methods; Chapter 6: Scattered Data Interpolation; Chapter 7: Scattered Data Fitting; Chapter 8: Shape Control; Chapter 9: Boundary-Value Problems; Chapter 10: Spherical Splines; Chapter 11: Applications of Spherical Splines; Bibliography; Script Index; Function Index; Subject Index.