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Inequalities for the maximal eigenvalue of a nonnegative matrix

Published online by Cambridge University Press:  18 May 2009

Lina Yeh
Affiliation:
Department of Mathematics, Soochow University, Taipei, Taiwan11102
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Abstract

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Two-sided bounds are obtained for the maximal eigenvalue of a positive matrix by iterating computations of row sums. The result provides an algorithm for approximating the maximal eigenvalue of a nonnegative matrix.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

REFERENCES

1.Kolotilina, L. Y., Lower bounds for the Perron root of a nonnegative matrix, Linear Algebra and Appl. 180 (1993), 133151.Google Scholar
2.Liu, S. L., Bounds for the greatest characteristic root of a nonnegative matrix, Linear Algebra and Appl. 239 (1996), 151160.CrossRefGoogle Scholar
3.Marcus, M. and Mine, H., Modern university algebra (Macmillan, New York, 1965).Google Scholar
4.Mine, H., Nonnegative matrices (John Wiley and Sons, New York, 1988).Google Scholar
5.Rojo, O. and Jimenez, R., A decreasing sequence of upper-bounds for the Perron root, Computer Math. Appl. No 8, 28 (1994), 915.Google Scholar
6.Wilkinson, J. H., The algebraic eigenvalue problem (Oxford Univ. Press, 1992).Google Scholar