Updating QR factorization procedure for solution of linear least squares problem with equality constraints

Journal of inequalities and applications

Salman Zeb¹ 

关键词: QR factorization;    orthogonal transformation;    updating;    least squares problems;    equality constraints;    65-XX;    65Fxx;    65F20;    65F25;   

DOI  :  10.1186/s13660-017-1547-0

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, we present a QR updating procedure as a solution approach for linear least squares problem with equality constraints. We reduce the constrained problem to unconstrained linear least squares and partition it into a small subproblem. The QR factorization of the subproblem is calculated and then we apply updating techniques to its upper triangular factor R to obtain its solution. We carry out the error analysis of the proposed algorithm to show that it is backward stable. We also illustrate the implementation and accuracy of the proposed algorithm by providing some numerical experiments with particular emphasis on dense problems.

【 授权许可】

CC BY