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Noda iterations for generalized eigenproblems following Perron-Frobenius theory. (English) Zbl 07037512

The authors propose two new variants for the Noda iteration to compute a generalized eigenvalue in the interval \((0,1)\) with a unit positive eigenvector. This approach follows the Perron-Frobenius theorem and has an important application to economic models. The methods are the modified Noda iteration (MNI) and the generalized Noda iteration (GNI). It is proved that both methods always converge and have quadratic asymptotic convergence rate. Some numerical examples are provided to illustrate the proposed methods.

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices

Software:

JDQR; JDQZ
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Full Text: DOI

References:

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