On the Invariance of the Interpolation Points of the Discrete $l_{1}$-approximation

ID
TR-77-01
Authors
Uri Ascher
Publishing date
February 1977
Length
14 pages
Abstract

Consider discrete $l_{1}$-approximations to a data function f, on some finite set of points X, by functions from a linear space of dimension m. We investigate the invariance of the interpolation points of the discrete $l_{1}$-approximation under a change in the approximated function. Conditions are given, under which the interpolant to a function g on a set of "best $l_{1}$ points" of a function f is a best $l_{1}$-approximant to g. Additional results are then obtained for the particular case of spline $l_{1}$-approximation.