Asymptotic error estimate for general Newton-type methods and its application to differential equations
Kulikov, Gennady Yu; Merkulov, A.I.; Shindin, S.K.
Russian Journal of Numerical Analysis and Mathematical Modelling, 22(6) (2007), 567-590
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.