Abstract
The paper is motivated by the paper of Khilnani and Tse (1985), ‘A fixed point algorithm with economic applications’, Journal of Economic Dynamics and Control 9, 125–137, where the method of updated successive approximations (USA) for the numerical solution of systems of nonlinear equations is presented. Some numerical examples show that the convergence statement of the USA method, which one can consider as a nonstationary extrapolation method, contains a flaw. In this paper we give some of these examples and discuss the variable extrapolation parameter used in the above cited paper, which cannot guarantee the convergence of the USA method. We also describe a nonlinear extrapolation method for solving nonlinear systems and give some sufficient conditions for the convergence of this method.
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