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Noda iterations for generalized eigenproblems following Perron-Frobenius theory.
- Source :
-
Numerical Algorithms . Mar2019, Vol. 80 Issue 3, p937-955. 19p. - Publication Year :
- 2019
-
Abstract
- In this paper, we investigate the generalized eigenvalue problem Ax = λBx arising from economic models. Under certain conditions, there is a simple generalized eigenvalue ρ(A, B) in the interval (0, 1) with a positive eigenvector. Based on the Noda iteration, a modified Noda iteration (MNI) and a generalized Noda iteration (GNI) are proposed for finding the generalized eigenvalue ρ(A, B) and the associated unit positive eigenvector. It is proved that the GNI method always converges and has a quadratic asymptotic convergence rate. So GNI has a similar convergence behavior as MNI. The efficiency of these algorithms is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]
- Subjects :
- *EIGENVECTORS
*THEORY
Subjects
Details
- Language :
- English
- ISSN :
- 10171398
- Volume :
- 80
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Numerical Algorithms
- Publication Type :
- Academic Journal
- Accession number :
- 135394732
- Full Text :
- https://doi.org/10.1007/s11075-018-0512-4