# Computing best discrete least-squares approximations by first-degree splines with free knots

## TL;DR

This paper introduces an algorithm for finding the optimal least-squares approximation of discrete functions using first-degree splines with free knots, ensuring a global best fit after finite steps, with practical applications demonstrated.

## Contribution

The paper presents a novel finite-step algorithm for computing globally optimal first-degree spline approximations with free knots for discrete data.

## Key findings

- Algorithm guarantees global optimality after finite steps
- Numerical examples demonstrate practical effectiveness
- Applications include medical data approximation

## Abstract

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).