Multivariate Spline Functions and Their Applications

As is known, the book named "Multivariate spline functions and their applications" has been published by the Science Press in 1994. This book is an English edition based on the original book mentioned 1 above with many changes, including that of the structure of a cubic - interpolation in n-dimensional spline spaces, and more detail on triangu lations have been added in this book. Special cases of multivariate spline functions (such as step functions, polygonal functions, and piecewise polynomials) have been examined math ematically for a long time. I. J. Schoenberg (Contribution to the problem of application of equidistant data by analytic functions, Quart. Appl. Math., 4(1946), 45 - 99; 112 - 141) and W. Quade & L. Collatz (Zur Interpo lations theories der reellen periodischen function, Press. Akad. Wiss. (PhysMath. KL), 30(1938), 383- 429) systematically established the the ory of the spline functions. W. Quade & L. Collatz mainly discussed the periodic functions, while I. J. Schoenberg's work was systematic and com plete. I. J. Schoenberg outlined three viewpoints for studing univariate splines: Fourier transformations, truncated polynomials and Taylor ex pansions. Based on the first two viewpoints, I. J. Schoenberg deduced the B-spline function and its basic properties, especially the basis func tions. Based on the latter viewpoint, he represented the spline functions in terms of truncated polynomials. These viewpoints and methods had significantly effected on the development of the spline functions.

List of contents

1 Introduction to Multivariate Spline Functions.- 2 Multivariate spline spaces.- 3 Other methods for studying multivariate spline functions.- 4 Higher-dimensional spline spaces.- 5 Rational spline functions.- 6 Piecewise algebraic curves and surfaces.- 7 Applications of multivariate spline functions in finite element method and CAGD.- References.

Product details

• Authors: Ren-Hong Wang, Ren-Hong Wang, Ren-Hong Wang
• Publisher: Springer Netherlands
• Languages: English
• Product format: Hardback
• Released: 26.06.2009
• EAN: 9780792369677
• ISBN: 978-0-7923-6967-7
• No. of pages: 512
• Weight: 912 g
• Illustrations: XII, 512 p.
• Series: Mathematics and Its Applications; Mathematics and Its Applications
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; C, Computer Vision, Image Processing and Computer Vision, Mathematics and Statistics, Engineering Design, Computational Mathematics and Numerical Analysis, Technical design, Computer mathematics, Numerical analysis, Mathematical theory of computation, Optical data processing, Image processing, Numeric Computing, Approximations and Expansions, Approximation theory