Global Smoothness and Shape Preserving Interpolation by Classical Operators

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Springer Science & Business Media, Sep 10, 2006 - Mathematics - 146 pages
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This monograph examines in detail two aspects in the field of interpolation of functions -the Global Smoothness Preservation Property (GSPP) and the Shape Preservation Property (SPP). By considering well-known classical interpolation operators such as Lagrange, Grünwald, Hermite-Fejér and Shepard type, the study is mainly developed for the univariate and bivariate cases. One of the first books on the subject, it presents to the reader, recent work featuring many new interesting results in this field, including an excellent survey of past research. Accompanied by numerous open problems, an updated set of references, and an appendix featuring illustrations of nine types of Shepard surfaces, this unique text is best suited to graduate students and researchers in mathematical analysis, interpolation of functions, pure and applied mathematicians in numerical analysis, approximation theory, data fitting, computer aided geometric design, fluid mechanics, and engineering researchers.

 

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Contents

Partial Shape Preservation Univariate Case 43
42
Global Smoothness Preservation Bivariate Case
71
Partial Shape Preservation Bivariate Case
91
Graphs of Shepard Surfaces
129
Index
145
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