# A METHOD FOR SOLVING LEAST-SQUARES PROBLEMS ARISING FROM ANGULAR LINEAR PROGRAMS

## Main Article Content

## Abstract

The most costly part of interior point methods for solving linear pro- gramming prbblems is in solving least squares subproblems. If the normal equation matrix of a least-squares problem is not nearly singular, it is well known that LDU decomposition is a stable method. However, for the nearly singular case, it can cause numerical difficulties. In this paper, we consider the linear proogram whose constraint matrix $B$ is large, sparse, and with angular structure. We assume that the normal equation matrices arising from such a linear program may be nearly singular. We present a numerically stable block method utilizing LDU decom- position wit5 diagonal pivoting for solving such normal equations. Although the method of the diagonal pivoting is old, this paper presents new results when the method is applied to the positive definite but nearly singular case.

## Article Details

*Tamkang Journal of Mathematics*,

*25*(1), 1–13. https://doi.org/10.5556/j.tkjm.25.1994.4419

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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