Reconstructions that combine interpolation with least squares fitting

•We develop a reconstruction that combines interpolation and least squares fitting.•We study the smoothness properties of the reconstruction and its approximation order.•We present some numerical examples where we compare different results.

We develop a reconstruction that combines interpolation and least squares fitting for point values in the context of multiresolution a la Harten. We study the smoothness properties of the reconstruction as well as its approximation order. We analyze how different adaptive techniques (ENO, SR and WENO) can be used within this reconstruction. We present some numerical examples where we compare the results obtained with the classical interpolation and the interpolation combined with least-squares approximation.