Abstract
In this article, we consider the nonlinear matrix equation arising in an interpolation problem. We use the Thompson metric to prove that the matrix equation always has a unique positive definite solution. An iterative method is constructed to compute the unique positive definite solution and its error estimation formula is given. Based on the matrix differentiation, we give a precise perturbation bound for the unique positive definite solution. The new results are illustrated by some numerical examples in the end.
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