# Fitting Continuous Piecewise Linear Functions

## Introduction

Continuous piecewise linear functions (CPWL) are an interesting class of functions.
The attractive features include their efficiency and continuity. The CPWL function
regression can be better behaving than the polynomial regression, and is
often used for approximation of complex functions. The CPWL functions are quite
efficient in terms of the computational and memory requirements, which allows
demanding applications, such as resource-constrained microcontrollers or graphics
processing.

However, there seems to be a lack of methods of fitting the CPWL
functions to other functions or experimental sets of data. In particular,
when the x coordinates of the CPWL function segments are fixed and only the
y coordinates are unknown. The following paper offers a solution to this
problem.

**Least-squares Fit of a Continuous Piecewise Linear Function**

## Abstract

The paper describes an application of the least-squares method to fitting a
continuous piecewise linear function. It shows that the solution is unique and
the best fit can be found without resorting to iterative optimization techniques.

### MATLAB function(s)

fitPiecewiseLinearFunction.m

Page created: 3-Sep-2004. Last updated: 3-Sep-2004