Point estimation of root finding methods (Q930436)

In this book, the author presents the basic concepts for convergent root finding methods and studies estimations of zero finding methods from data at one point using Smale's point estimation theory, by constructing such initial conditions, providing guaranteed convergence. Furthermore the author proposes the construction of computationally verifiable initial conditions and studies the corresponding convergence analysis of the simultaneous methods, which predict the immediate appearance of the guaranteed and fast convergence of iterative root finding methods. Additionally, the author presents higher order families of simultaneous methods for the determination of polynomial (simple or multiple) zeros. Finally, numerical results, illustrating the convergence behavior, are presented.