%A P. S. Bradley
%A O. L. Mangasarian
%A J. B. Rosen
%T Parsimonious Least Norm Approximation
%D March 1997
%R 97-03
%I COMPUTER SCIENCES DEPARTMENT, UNIVERSITY OF WISCONSIN
%C MADISON, WI
%X
A theoretically justifiable fast finite successive linear approximation
algorithm is proposed for obtaining a parsimonious solution
to a corrupted linear system $Ax=b+p$, where the corruption
$p$ is due to noise or error in measurement. The proposed
linear-programming-based algorithm finds a solution $x$
with minimal cardinality
which satisfies the given system as best as possible.
Numerical tests on a signal-processing-based example
indicate that the proposed method is superior by
orders of magnitude to a least squares solution
as well as to a solution obtained by combinatorially
choosing a solution with minimal cardinality.