Generalized Ostrowski root-finding method

摘要

We adapt the classical Ostrowski method for the simultaneous determination of all zeros of generalized polynomials constructed by the functions from Tchebyshev's system. It is shown that the order of convergence of this method is 3. The numerical stability of the method in the presence of rounding errors and a posteriori error bound, which can be regarded as a generalization of Laguerre's classical result for a polynomial, is analyzed. Numerical examples are included.