Multivariate Spline Functions and Their Applications

Wang, Renhong; Wang, Ren-Hong

ISBN 10: 079236967X / ISBN 13: 9780792369677

Published by Springer, 2001

About this Item

Seller Inventory # 971291-n

Bibliographic Details

• Title: Multivariate Spline Functions and Their Applications
• Publisher: Springer
• Publication Date: 2001
• Language: English
• ISBN 10: 079236967X
• ISBN 13: 9780792369677
• Binding: Hardcover
• Condition: New

About this title

Synopsis

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.

Synopsis

This book deals with the algebraic geometric method of studying multivariate splines. The topics treated include: the theory of multivariate spline spaces, higher-dimensional splines, rational splines, piecewise algebraic variety (including piecewise algebraic curves and surfaces), applications in the finite element method, and, computer-aided geometric design. Many new results are given. This volume will be of interest to researchers and graduate students whose work involves approximations and expansions, numerical analysis, computational geometry, image processing and CAD/CAM.