TY - JOUR
AU - YANG, EUGENE K.
AU - CHOU, CHIA-HSIANG
PY - 1994/03/01
Y2 - 2024/08/16
TI - A METHOD FOR SOLVING LEAST-SQUARES PROBLEMS ARISING FROM ANGULAR LINEAR PROGRAMS
JF - Tamkang Journal of Mathematics
JA - Tamkang J. Math.
VL - 25
IS - 1
SE - Papers
DO - 10.5556/j.tkjm.25.1994.4419
UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/4419
SP - 1-13
AB - <div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">The most costly part of interior point methods for solving linear pro- gramming prbblems is in solving least squares subproblems. </span><span style="font-size: 9.000000pt; font-family: 'TimesNewRomanPSMT';">If </span><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">the normal equation matrix of a le</span><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">ast-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 $</span><span style="font-size: 11.000000pt; font-family: 'TimesNewRomanPS'; font-style: italic;">B$ </span><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">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. </span></p></div></div></div>
ER -