Departmental Papers (ESE)


The class of continuous piecewise linear (PL) functions represents a useful family of approximants because invertibility can be readily imposed, and if a PL function is invertible, then it can be inverted in closed form. Many applications, arising, for example, in control systems and robotics, involve the simultaneous construction of a forward and inverse system model from data. Most approximation techniques require that separate forward and inverse models be trained, whereas an invertible continuous PL affords, simultaneously, the forward and inverse system model in a single representation. The minvar algorithm computes a continuous PL approximation to data. Local convergence of minvar is proven for the case when the data generating function is itself a PL function and available directly rather than through data.

Document Type

Journal Article

Subject Area

GRASP, Kodlab

Date of this Version

March 2003


Reprinted from SIAM Journal on Numerical Analysis, Volume 41, Issue 3, 2003, pages 87-93.
Publisher URL:

NOTE: At the time of publication the author, Daniel Koditschek, was affiliated with the University of Michigan. Currently, he is a faculty member of the School of Engineering at the University of Pennsylvania.


piecewise linear, invertible approximation, moving mesh, triangulation



Date Posted: 03 April 2008

This document has been peer reviewed.