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, Grünwald, Hermite-Fejér 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.