Multivariate Spline Functions and Their Applications

Ren-Hong Wang (Autor)

Buch | Softcover

512 Seiten

2010 | Softcover reprint of hardcover 1st ed. 2001
Springer (Verlag)
978-90-481-5703-7 (ISBN)

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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.

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.

Erscheint lt. Verlag	9.12.2010
Reihe/Serie	Mathematics and Its Applications ; 529
Zusatzinfo	XII, 512 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Informatik ► Grafik / Design ► Digitale Bildverarbeitung
	Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
	Mathematik / Informatik ► Mathematik ► Analysis
	Technik
ISBN-10	90-481-5703-X / 904815703X
ISBN-13	978-90-481-5703-7 / 9789048157037
Zustand	Neuware