OEIG swMATH ID: 7166 Software Authors: Das, Saptarshi; Neumaier, Arnold Description: 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/ neum/software/oeig/. Homepage: http://www.mat.univie.ac.at/~neum/software/oeig/ Keywords: overdetermined eigenvalue problem; numerical linear algebra Related Software: Matlab; Chebfun; JDQZ; Eigtool; GaussQR; LSMR; CIRR; FEAST; LSQR Cited in: 5 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Solving overdetermined eigenvalue problems. Zbl 1266.45003Das, Saptarshi; Neumaier, Arnold 2013 all top 5 Cited by 9 Authors 1 Cuyt, Annie A. M. 1 Das, Saptarshi 1 De Lathauwer, Lieven 1 Hashemi, Behnam 1 Lee, Wen-shin 1 Morikuni, Keiichi 1 Nakatsukasa, Yuji 1 Neumaier, Arnold 1 Stegeman, Alwin Cited in 4 Serials 2 SIAM Journal on Scientific Computing 1 SIAM Journal on Matrix Analysis and Applications 1 Applied and Computational Harmonic Analysis 1 Computational Methods in Applied Mathematics all top 5 Cited in 7 Fields 5 Numerical analysis (65-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 1 Commutative algebra (13-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Operator theory (47-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year