Approximation by Quasi-Interpolants, their Representation as Differential Operators and Applications
by
Detlef H. Mache
University of Dortmund, Germany

Most of the known quasi-interpolants of order n leave invariant the space of polynomials of degree at most n. Here we present the differential forms of these linear isomorphism and of their inverses for different generalized methods and extensions. Therefore the polynomial sequences (and the intermediate types) can be computed by recurrence relations, which allow to study the approximation properties. For the polynomial coefficients of the associated linear differential methods one can give an interesting connection to orthogonal polynomials.

References
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Date received: February 6, 2002