NAApr 19, 2017
Discrete approximation by first-degree splines with free knotsLudwig J. Cromme, Jens Kunath
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 ($1 \leq p \leq \infty)$. 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.
NAApr 19, 2017
Computing best discrete least-squares approximations by first-degree splines with free knotsLudwig J. Cromme, Jens Kunath, Andreas Krebs
We present an algorithm to compute best least-squares approximations of discrete real-valued functions by first-degree splines (broken lines) with free knots. We demonstrate that the algorithm delivers after a finite number of steps a (global) best approximation. The analysis is complemented by remarks on programming and by a number of numerical examples including applications from medicine (MBC, MIC).