Asymptotic error estimate of iterative Newton-type methods and its practical application

Lecture Notes in Computer Science, 3045 (2004), 667-675
http://dx.doi.org/10.1007/978-3-540-24767-8_70

In the paper we present a new result for evaluating the convergence error of iterative Newton-type methods with respect to the number of iteration steps. We prove an explicit asymptotically correct estimate that provide a fruitful basis to treat many practical situations. As an example of such application, we solve three important problems arising in numerical integration of ordinary differential equations and semi-explicit index 1 differential-algebraic systems.