On the optimal knots of first degree splines

Suppose that f is an element of C[a,b] is a strictly convex function. Let U = {u(0),..., u(n)} be a set of knots on [a,b], and S(U,.) the linear spline with knots set U. In this paper we consider best L-1-approximation with at most n-1 varying partition points a=u(0) < u(1) <...<u(n)=b. A novel algorithm is given to obtain optimal knots of L-1-approximation. starting with any of knot-set U-(0), we construct a sequence of knot-sets U-(i). The corresponding sequence of linear splines SW are constructed such that the corresponding sequence of L-1-errors will be a decreasing one.