Multiplicative schemas in iterative algorithms. I: Nonlinear equations (Q1899664)

For the numerical solution of systems of nonlinear equations, the author investigates multiplicative iterative schemes of the form \(x^{k+1} = x^k \otimes p(x^k,\gamma)\) where \(p(\cdot, \cdot)\) is a correcting operator with a controlling parameter and \(\otimes\) denotes componentwise multiplication. Such schemes are motivated by methods for the solution of entropy maximization problems in stochastic communication systems. The main result of the paper states necessary conditions for the convergence of the iterative processes.