×

zbMATH — the first resource for mathematics

An algorithm of diagonal transformation for Perron root of nonnegative irreducible matrices. (English) Zbl 1095.65030
For computing the spectral radius of a nonnegative matrix, a class of diagonal transformation methods proposed by W. Bunse [SIAM J. Numer. Anal. 18, 693–704 (1981; Zbl 0478.65017)] can be used. One of these methods is the completely diagonal transformation method. The contribution of this paper is that the convergence of this method for nonnegative irreducible matrices is proved.

MSC:
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
PDF BibTeX Cite
Full Text: DOI
References:
[1] Horn, R.A.; Johnson, C.R., Matrix analysis, (1985), Cambridge University Press · Zbl 0576.15001
[2] Bunse, Wolfgang, A class of diagonal transformation methods for the computation of the spectral radius of a nonnegative matrix, SIAM J. numer. anal., 18, 4, 693-704, (1981) · Zbl 0478.65017
[3] Rojo, O.; Soto, R., Perron root bounding for nonnegative persymmetric matrices, Comput. math. appl., 31, 12, 69-76, (1996) · Zbl 0857.15010
[4] Szyld, D., A sequence of lower bounds for the spectral redius of nonnegative matrices, Linear algebra appl., 174, 239-242, (1992) · Zbl 0758.15013
[5] Dursun, T.; Kirkland, S., A sequence of upper bounds for the Perron root of a nonnegative matrix, Linear algebra appl., 273, 23-28, (1998) · Zbl 0901.15012
[6] Meyer, C.D., Uncoupling the Perron eigenvector problem, Linear algebra appl., 114, 69-94, (1989) · Zbl 0673.15006
[7] Neumann, M., Inverse of Perron complements of inverse M-matrices, Linear algebra appl., 313, 163-171, (2000) · Zbl 0959.15023
[8] Lu, L.Z., Perron complement and Perron root, Linear algebra appl., 341, 239-249, (2002) · Zbl 0999.15009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.