On monosplines of least deviation

be k given real numbers, and n a non-negative integer. Let the function S be defined in each of the intervals (o, t,), 1, ~2), * *, [(k, co) by a separate polynomial of degree not exceeding n, so that the composite function S be continuous together with its first n -1 derivatives (no continuity requirement for n = 0). S(n) is a step-function with (possible) discontinuities at the points (1). A function S of this kind is called a spline function [7 of class (n, k), the points (1) being referred to as its knots. It is convenient to introduce the notation