Computing best discrete least-squares approximations by first-degree splines with free knots
Provides a guaranteed global optimization method for a specific spline fitting problem, but is incremental as it addresses a known problem with a new algorithm.
The paper presents an algorithm for computing best least-squares approximations of discrete functions using first-degree splines with free knots, guaranteeing a global best approximation in finite steps, with applications in medicine.
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).