Lacunary Interpolation at Odd and Even Nodes

Abstract

Here a special (0, 2; 0, 3) lacunary interpolation scheme is considered where the data are prescribed unevenly at even and odd nodes of an arbitrarily defined partition of the unit interval I =[0,1].The problem described as, we have the function values and second derivatives at odd nodes, whereas function values and the thirdderivatives ateven nodes are known, weproved that there existsa unique quantic spline of continuity class C 2 by solving the above mentioned interpolation scheme.Furthermore, it is also proved that this spline function converges to the given function with the desired order of accuracy.