Multivariate Spline Functions and Their Applications

Multivariate Spline Functions and Their Applications

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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.
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Product details

  • Hardback | 512 pages
  • 167.6 x 246.4 x 33mm | 907.2g
  • Dordrecht, Netherlands
  • English
  • 2001 ed.
  • XII, 512 p.
  • 079236967X
  • 9780792369677

Table 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. Index.
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