Spline Functions: Computational Methods

Describing in detail the key algorithms needed for computing with spline functions, this book illustrates the usefulness of splines 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. 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 licence, which can be used to run all of the examples in the book and provides readers with the essential tools 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.

Larry Schumaker was a Professor of Mathematics at both the University of Texas, Austin, and Texas A&M University, and since 1988 has been the Stevenson Professor of Mathematics at Vanderbilt University. He is a SIAM Fellow and a Member of the Norwegian Academy of Sciences. In addition to editing 40 conference proceedings and translating a number of books from German, he is the author of Spline Functions: Basic Theory, and a coauthor of Spline Functions on Triangulations. His research continues to focus on spline functions and their applications.