This monograph examines and develops the Global Smoothness
Preservation Property (GSPP) and the Shape Preservation Property
(SPP) in the field of interpolation of functions. The study is
developed for the univariate and bivariate cases using well-known
classical interpolation operators of Lagrange, GrA1/4nwald,
Hermite-FejA(c)r and Shepard type. One of the first books on the
subject, it presents interesting new results alongwith an excellent
survey of past research.
Key features include:
- potential applications to data fitting, fluid dynamics, curves
and surfaces, engineering, and computer-aided geometric design
- presents recent work featuring many new interesting results as
well as an excellent survey of past research
- many interesting open problems for future research presented
throughout the text
- includes 20 very suggestive figures of nine types of Shepard
surfaces concerning their shape preservation property
- generic techniques of the proofs allow for easy application to
obtaining similar results for other interpolation operators
This unique, well-written 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.
General
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