Solving overdetermined eigenvalue problems. We propose a new interpretation of the generalized overdetermined eigenvalue problem (π-Ξ»π)π―β0 for two mΓn(m>n) matrices π and π, its stability analysis, and an efficient algorithm for solving it. Usually, the matrix pencil {π-Ξ»π} does not have any rank deficient member. Therefore we aim to compute Ξ» for which π-Ξ»π is as close as possible to rank deficient; i.e., we search for Ξ» that locally minimize the smallest singular value over the matrix pencil {π-Ξ»π}. Practically, the proposed algorithm requires πͺ(mn 2 ) operations for computing all the eigenpairs. We also describe a method to compute practical starting eigenpairs. The effectiveness of the new approach is demonstrated with numerical experiments. A MATLAB-based implementation of the proposed algorithm can be found at http://www.mat.univie.ac.at/Β neum/software/oeig/.

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