Adaptive interpolation with maximum order close to discontinuities

Adaptive rational interpolation has been designed in the context of image processing as a new nonlinear technique that avoids Gibbs phenomenon when we approximate discontinuous function. In this work, present generalization to method giving explicit expressions for all weights any order algorithm. It similar behavior weighted essentially non oscillatory (WENO) but design case is more simple. Also, propose way construct them obtaining maximum near discontinuities. Some experiments are performed demonstrate our results and compare with standard methods.