Effect of polynomial shift in the method for finding the largest eigenvalue of a polynomial (IR)

Nurul Akmal Mohamed

QR Code Link :
Type :	article
Subject :	Q Science (General)
ISSN :	1816-949X
Main Author :	Nurul Akmal Mohamed
Additional Authors :	N.F. Ibrahim
Title :	Effect of polynomial shift in the method for finding the largest eigenvalue of a polynomial (IR)

Place of Production :	Medwell Journals
Year of Publication :	2017
PDF Full Text :	The author has requested the full text of this item to be restricted.

Abstract :

A new method for finding the largest eigenvalue of a generalised nonnegative polynomial was introduced in 2014 by Ibrahim. The method was proven to be convergent for weakly irreducible polynomials. In the method, an irreducible polynomial is shifted such that it becomes primitive. However, it is illlkno\Vll what is the optimal shift and the effect of the step length to the method. In this study we examine the effect of the step leugtli to tlie metliod.

References

1. Chang. K.C.. K. Pearson and T. Zhang. 2008. Perron-frobenius theorem for nonnegative tensors. Commun. Math. Sci.• 6: 507-520. 2. Chang. K.C .• K.J. Pearson and T. Zhang. 2011. Primitivity the convergence of the NQZ method and the largest eigenvalue for nonnegative tensors. SIAM J. Matrix Ami. Appl.. 32: 806-819. 3. Friedland. S.• S. Gaubert and L. Han. 2013. Perron frobenius theorem for nonnegative multilinear forms and extensions.Linear Algebra Appl. 438: 738-7 49. 4. Gaubert. S. and J. Gumwardem. 2004. The perron frobenius theorem for homogeneous, monotone functions. Trans. Am. Math. Soc.• 356: 4931-4950. 5. Ibrahim. N.F.. 2014. An algorithm for the largest eigenvalue of nonhomogeneous nonnegative polynomials. Numer. Algebra Control Optim .• 4: 75-91. 6. Jacobi. M.N. and P.R. Jonsson, 2011. Optimal networks of nature reserves can be fmmd through eigenvalue perturbation theory of the connectivity matrix. Ecol. Appl.. 21: 1861-1870. 7. Liu. Y.. G. Zhou and N.F. Ibrahim. 2010. An always convergent algorithm for the largest eigenvalue of an irreducible nonnegative tensor. J. Comput. Appl. Math .• 235: 286-292. 8. Ng. M.• L. Qi and G. Zhou, 2009. Finding the largest eigenvalue of a nonnegative tensor. SIAM J. Matrix Ami. Appl.. 31: 1091-1099. 9. Soares, C.G. and W. Fricke, 2011. Advances in Marine Structures. CRC Press, Boca Raton, Florida, ISBN-13:978-0-203-80811-5. Pages: 730. 10. Varga, R., 1965. Matrix Iterative Analysis. Prentice Hall, Englewood Cliffs. New Jersey •.

This material may be protected under Copyright Act which governs the making of photocopies or reproductions of copyrighted materials.
You may use the digitized material for private study, scholarship, or research.

Back to previous page