A modified Newton iteration for finding nonnegative Z-eigenpairs of a nonnegative tensor
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We propose a modified Newton iteration for finding some nonnegative Z-eigenpairs of a nonnegative tensor. When the tensor is irreducible, all nonnegative eigenpairs are known to be positive. We prove local quadratic convergence of the new iteration to any positive eigenpair of a nonnegative tensor, under the usual assumption guaranteeing the local quadratic convergence of the original Newton iteration. A big advantage of the modified Newton iteration is that it seems capable of finding a nonnegative eigenpair starting with any positive unit vector. Special attention is paid to transition probability tensors.
KeywordsNonnegative tensor Transition probability tensor Nonnegative Z-eigenpair Modified Newton iteration Quadratic convergence
Mathematics Subject Classification (2010)65F15 65F50
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The authors thank the two referees for their helpful comments. This work was started when C.-H. Guo visited ST Yau Center at Chiao-Da in Taiwan in late 2015; he thanks the Center for its hospitality.
- 9.Hu, S., Huang, Z.-H., Qi, L.: Finding the spectral radius of a nonnegative tensor. arXiv:1111.2138v1 (2011)
- 19.Varga, R.S.: Matrix iterative analysis. Springer (2000)Google Scholar
- 20.Yang, Y., Yang, Q.: On some properties of nonnegative weakly irreducible tensors. arXiv:1111.0713v2 (2011)