English

Discrete approximation by first-degree splines with free knots

Numerical Analysis 2017-04-20 v1

Abstract

This paper deals with the approximation of discrete real-valued functions by first-degree splines (broken lines) with free knots for arbitrary LpL_p-norms (1p)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 L2L_2-norm.

Keywords

Cite

@article{arxiv.1704.05668,
  title  = {Discrete approximation by first-degree splines with free knots},
  author = {Ludwig J. Cromme and Jens Kunath},
  journal= {arXiv preprint arXiv:1704.05668},
  year   = {2017}
}
R2 v1 2026-06-22T19:21:12.999Z