We propose a new combination of the bivariate Shepard operators  by the three point Lidstone polynomials introduced in . The new combination inherits both degree of exactness and Lidstone interpolation conditions at each node, which characterize the interpolation polynomial. These new operators …nd application to the scattered data interpolation… (More)
OBJECTIVES To generate and validate a murine model of joint surface repair following acute mechanical injury. METHODS Full thickness defects were generated in the patellar groove of C57BL/6 and DBA/1 mice by microsurgery. Control knees were either sham-operated or non-operated. Outcome was evaluated by histological scoring systems. Apoptosis and… (More)
The algebraic polynomial interpolation on uniformly distributed nodes is affected by the Runge phenomenon, also when the function to be interpolated is analytic. Among all techniques that have been proposed to defeat this phenomenon , there is the mock-Chebyshev interpolation which is an interpolation made on a subset of the given nodes which elements mimic… (More)
We show how to combine local Shepard operators with Hermite polynomials on the simplex (Chui and Lai, 1990 ) so as to raise the algebraic precision of the Shepard-Taylor operators (Farwig, 1986 ) that use the same data and contem-poraneously maintain the interpolation properties at each sample point (derivative data included) and a good accuracy of… (More)
We use basic results of general theory of …nite interpolation and linear algebra in order to prove the nonsingularity of a special class of cen-trosymmetric matrices arising in spectral methods in BVPs .
We introduce the Shepard–Bernoulli operator as a combination of the Shepard operator with a new univariate interpolation operator: the generalized Taylor polynomial. Some properties and the rate of convergence of the new combined operator are studied and compared with those given for classical combined Shepard operators. An application to the interpolation… (More)