Discrete approximation by first-degree splines with free knots

Publication date: 19 April 2017

Abstract: This paper deals with the approximation of discrete real-valued functions by first-degree splines (broken lines) with free knots for arbitrary

L_{p}

-norms (

1 l e q p l e q i n f t y)

. We prove the existence of best approximations und derive statements on the position of the (free) knots of a best approximation. Building on this, elsewhere we develop an algorithm to determine a (global) best approximation in the

L_{2}

-norm.

This page was built for publication: Discrete approximation by first-degree splines with free knots