Least-squares computation of eigenvectors and null vectors: an application of MINRES, GMRES and LSQR. |
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| For a singular matrix of arbitrary shape, we observe that null vectors can be obtained by solving least-squares problems involving the \emph{transpose} of the matrix. For sparse rectangular matrices, this suggests a new application of the iterative solver LSQR. In the square case, MINRES, GMRES or LSQR are applicable. New stopping rules are needed for MINRES and GMRES on singular systems. Results are given for computing the stationary probability vector for Markov Chain models and null vectors for sparse systems arising in helioseismology. |
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algweb@cerfacs.fr Last Update: June 6, 2003 |