Discretization of implicit ODEs for singular root-finding problems
The iteration generated by the numerical integration of an ordinary differential equation (ODE) may be studied as a discrete dynamical system. Starting from this fact, the paper considers different discretizations of continuous-time models for singular root-finding and optimization problems. The paper is devoted, firstly, to the use of discrete-time analysis techniques for singular problems, based on continuous-time stability and numerical stability and, secondly, to introduce a systematic methodology for the formulation of quadratically convergent iterations for singular root-finding problems.
scientific article; zbMATH DE number 1758454
scientific article