Abstract
In the paper we present a new result for evaluating the convergence rate of iterative Newton-type methods with respect to the number of iteration steps. We obtain an explicit asymptotically correct estimate that provides a fruitful basis for many practical situations. As examples of such applications, we solve four important problems arising in numerical integration of ordinary differential equations and index 1 semi-explicit differential-algebraic systems.
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More From: Russian Journal of Numerical Analysis and Mathematical Modelling
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