Column Relaxation Methods for Least Norm Problems

Abstract

The paper derives column relaxation schemes for calculating the $\ell _p $ solution of an inconsistent system of linear equations. The need for such methods arises when the system to be solved is large, sparse, and unstructured. Special attention is given to each of the cases $p = 1$, $1 < p < 2$, $2 < p < \infty $, and $p = \infty $. Numerical experiments illustrate the ability of the proposed schemes to handle large $\ell _1 $ and $\ell _\infty $ problems.