Abstract
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.
Original language | English |
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Pages (from-to) | 595-616 |
Number of pages | 22 |
Journal | Numerical Algorithms |
Volume | 80 |
Issue number | 2 |
DOIs | |
State | Published - 6 Feb 2019 |
Keywords
- Modified Newton iteration
- Nonnegative tensor
- Nonnegative Z-eigenpair
- Quadratic convergence
- Transition probability tensor