ABSTRACT
In light of many applications of interpolation methods, this chapter discusses the advanced interpolations of data for the uniform functions with continuity of their high-order derivatives with many abilities. This means that, in these interpolators, it is assumed that, assume that at the interpolation points, the value of the function 1 is equal to the value of the interpolation function, as well as the value of the finite derivatives of 2 is equal to the value of the finite derivatives of the interpolation function, and this is the reason for smoothness and accuracy of the interpolation function.
