On the matrix equation arising in an interpolation problem

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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