A stationary iterative pseudoinverse algorithm |
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Authors: | Tommy Elfving |
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Institution: | 1. Department of Mathematics, Link?ping University, S-581 83, Link?ping, Sweden
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Abstract: | Iterative methods applied to the normal equationsA
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.
This work was supported by the Swedish Research Council for Engineering Sciences, TFR. |
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Keywords: | 65F10 65F20 65F50 |
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