ABSTRACT

This chapter deals with algebraic interpolation. High sensitivity of algebraic interpolating polynomials to the errors in the tabulated values of f(x), as well as the “iffy” convergence of the sequence Pn(x, f) on uniform grids, prompt the use of piecewise polynomial interpolation. Reconstruction of continuous functions from discrete data is normally accompanied by the unavoidable error. This error is caused by the loss of information which inevitably occurs in the course of discretization. The unavoidable error is typically determined by the regularity of the continuous function and by the discretization parameters. If the accuracy of a given method is limited by its own design and does not, generally speaking, reach the level of the unavoidable error determined by the smoothness of the approximated function, then the method is said to be saturated by smoothness.