Discrete approximation by first-degree splines with free knots

2017/04/19 by Ludwig J. Cromme, Cromme, Ludwig J., Jens Kunath +1
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Digital Image Processing Techniques #FOS: Mathematics #Mathematical Approximation and Integration #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1704.05668

openalex publication_date 2017/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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 ≤ p ≤ ∞). 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 L₂-norm.

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