Computation of the stabilizing solution pair of a system of nonlinear matrix equations is of great interest in calculating the Green’s function of nanoparticles. By noting that each solution of the pair might have various sizes, an inversion-free iteration with dynamical parameters is proposed in this paper. Under proper assumptions the convergence of the algorithm is established, as well as the bound of the iteration sequence. Preliminary numerical experiments indicate that the dynamically parameterized inversion-free iteration is very efficient to compute the stabilizing solution pair.
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