A simple heuristic construction of good interpolation points on the unit disc is proposed. First, a set of quasi-random uniformly distributed points in the unit square is generated. Consequently, this set is transformed onto the unit sphere using cylindrical Lambert map and, finally, the points of the upper hemisphere are orthogonally projected onto the unit disc. Numerical results concerning i...

A general method for near-best approximations to functionals on Rd, using scattered-data information is discussed. The method is actually the moving least-squares method, presented by the Backus-Gilbert approach. It is shown that the method works very well for interpolation, smoothing and derivatives’ approximations. For the interpolation problem this approach gives Mclain’s method. The method ...

We consider the possibility of using locally supported quasi-interpolation operators for the approximation of univariate non-smooth functions. In such a case one usually expects the rate of approximation to be lower than that of smooth functions. It is shown in this paper that prior knowledge of the type of ’singularity’ of the function can be used to regain the full approximation power of the ...