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Complex shift and invert strategies for real matrices. (English) Zbl 0623.65045

Algorithms for the nonsymmetric eigenvalue problem \((F-\lambda M)X=0\) with real matrices are studied. It is shown that the symmetry around the real axis can be exploited in algorithms based on inverse iteration. Algorithm are developed which use either the real or the imaginary part of \((F-\lambda M)^{-1}M\), obtained by a complex banded Gaussian elimination. Numerical results are given for an example arising from a brusselator model of a tubular chemical reactor.
Reviewer: A.Ruhe

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
80A32 Chemically reacting flows
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