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 (πΞ»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 {πΞ»π} does not have any rank deficient member. Therefore we aim to compute Ξ» for which πΞ»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 {πΞ»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 MATLABbased 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 1266.45003 Das, Saptarshi; Neumaier, Arnold 
2013

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Cited by 9 Authors
1  Cuyt, Annie A. M. 
1  Das, Saptarshi 
1  De Lathauwer, Lieven 
1  Hashemi, Behnam 
1  Lee, Wenshin 
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 
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