Error estimation in numerical solution of equations and systems of equations
Abstract
In [7], [8], M. Urabe studies the numerical convergence and error estimation in the case of operatorial equation solution by means of iteration methods. Urabe's results refer to operatorial equations in complete metric spaces, while as application the numerical convergence of Newton's method in Banach spaces is studied. Using Urabe's results, M. Fujii [1] studies the same problems for Steffensen's method and the chord method applied to equations with real functions. In [6], Urabe's method is applied to a large class of iteration methods with arbitrary convergence order. We propose further down to extend Urabe's results to the case of the Gauss-Seidel method for systems of equations in metric spaces.
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