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Volume :29 Issue : 1 2002      Add To Cart                                                                    Download

On the optimal knots of first degree splines

Auther : H. HAMIDEH

Department of Mathematics, College of Science, King Saud University, P.O.Box 2455, Riyadh 11451. Saudi Arabia

ABSTRACT

Suppose that  f   C[a,b] is a strictly convex function. Let U= {u0, ..., un} be a set of knots on [a,b], and S(U,.) the linear spline with knots set U. In this paper we consider best L1-approximation with at most n-1 varying partition points a = u0 < u1 < ... <  un = b.

A novel algorithm is given to obtain optimal knots of L1-approximation, starting with any of knot-set U(0) we construct a sequence of knot-sets U(i). The corresponding sequence of linear splines S(i) are constructed such that the corresponding sequence of L1-errors will be a decreasing one.

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