# A stationary iterative pseudoinverse algorithm

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## Abstract

Iterative methods applied to the normal equations*A* ^{ T } *Ax=A* ^{ T } *b* are sometimes used for solving large sparse linear least squares problems. However, when the matrix is rank-deficient many methods, although convergent, fail to produce the unique solution of minimal Euclidean norm. Examples of such methods are the Jacobi and SOR methods as well as the preconditioned conjugate gradient algorithm. We analyze here an iterative scheme that overcomes this difficulty for the case of stationary iterative methods. The scheme combines two stationary iterative methods. The first method produces any least squares solution whereas the second produces the minimum norm solution to a consistent system.

### AMS subject classification

65F10 65F20 65F50### Key words

Stationary iterative methods least squares pseudoinverse solution## Preview

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