Spline Functions: Computational Methods - Hardcover

Schumaker, Larry L.

Hardcover

ISBN 10: 1611973899 ISBN 13: 9781611973891

Publisher: Society for Industrial and Applied Mathematics, 2016

Synopsis

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.

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.

Audience: This book is designed for mathematicians, engineers, scientists, and anyone else wanting to make use of spline functions for numerical computation.

Contents: 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.

About this title

Book Description

Focussing on key algorithms for computing with bivariate splines on triangulations in the plane and on the sphere, this book illustrates the usefulness of splines in solving problems in numerical analysis, including function approximation, numerical quadrature, data fitting, and the numerical solution of PDEs.

About the Author

Larry L. Schumaker was a professor of Mathematics at both the University of Texas in Austin and Texas A & M University and since 1988 has been the Stevenson Professor of Mathematics at Vanderbilt University. In 1978 he was a Humboldt fellow at the Free University of Berlin and in 1989 spent a year at Ludwig Maximilian University in Munich as a Humboldt prize winner. 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.

Edition details

• Publisher: Society for Industrial and Applied Mathematics
• Publication date: 2016
• ISBN 10: 1611973899
• ISBN 13: 9781611973891
• Binding: Hardcover
• Language: English
• Number of pages: 430