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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...
We consider the solution of large-scale Lyapunov and Stein equations. For Stein equations, the well-known Smith method will be adapted, with not explicitly computed but in the recursive form , and the fast growing but diminishing components in the approximate solutions truncated. Lyapunov equations will be first treated with the Cayley transform before the...
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