Global Smoothness and Shape Preserving Interpolation by Classical Operators
This monograph focuses on two aspects regarding the interpolation of functions: the Global Smoothness Preservation Property and Shape Preservation Property of well-known classical interpolation operators such as Lagrange, Gr nwald, Hermite-Fej r and Shepard type considering 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 as 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 for 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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