Volume 29, pp. 97-115, 2007-2008.

A rank-one updating approach for solving systems of linear equations in the least squares sense

A. Mohsen and J. Stoer

Abstract

The solution of the linear system $Ax=b$ with an $m\times n$-matrix $A$ of maximal rank $\mu :=min(m,n)$ is considered. The method generates a sequence of $n\times m$-matrices $H_k$ and vectors $x_k$ so that the $A{H}_k$ are positive semidefinite, the $H_k$ approximate the pseudoinverse of $A$ and $x_k$ approximate the least squares solution of $Ax=b$. The method is of the type of Broyden's rank-one updates and yields the pseudoinverse in $\mu$ steps.

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Key words

linear least squares problems, iterative methods, variable metric updates, pseudo-inverse

AMS subject classifications

65F10, 65F20