Positive spline operators and orthogonal splines
Journal of Approximation Theory
Box splines
Near minimally normed spline quasi-interpolants on uniform partitions
Journal of Computational and Applied Mathematics
On Chebyshev-type discrete quasi-interpolants
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
Near-best quasi-interpolants associated with H-splines on a three-direction mesh
Journal of Computational and Applied Mathematics
A general method for constructing quasi-interpolants from B-splines
Journal of Computational and Applied Mathematics
Computing quasi-interpolants from the B-form of B-splines
Mathematics and Computers in Simulation
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Spline quasi-interpolants on the real line are approximating splines to given functions with optimal approximation orders. They are called integral quasi-interpolants if the coefficients in the spline series are linear combinations of weighted mean values of the function to be approximated. This paper is devoted to the construction of new integral quasi-interpolants with compactly supported piecewise polynomial weights. The basic idea consists of minimizing an expression appearing in an estimate for the quasi-interpolation error. It depends on how well the quasi-interpolation operator approximates the first non-reproduced monomial. Explicit solutions as well as some numerical tests in the B-spline case are given.