On linear interpolation under interval data

Some results related to the problem of interpolation of n vertical segments (xk, Yk), k = 1,…,n, in the plane with generalized polynomial functions that are linear combinations of m basic functions are presented. It is proved that the set of interpolating functions (if not empty) is bounded in every subinterval (xk, xk+1) by two unique such functions ηk− and ηk+. An algorithm with result verification for the determination of the boundary functions ηk−, ηk+ and for their effective tabulation is reported and some examples are discussed.