The convergence of a family of parallel zero-finding methods
The aim of the paper is to introduce computationally verifiable initial conditions which could guarantee the convergence of the recently introduced class of fourth-order methods [cf. \textit{T. Sakurai} and \textit{M. S. Petković}, J. Comput. Appl. Math. 72, 275--291 (1996; Zbl 0859.65048)] for simultaneous finding polynomial zeros. First, the authors introduce some basic facts on circular complex arithmetic. Then they prove several technical lemmas. Finally, they state two significant theorems concerning the initial conditions for the convergence. These conditions depend only on polynomial coefficients, its degree and initial approximations of zeros, thus they can be easily verified.
scientific article; zbMATH DE number 2142473
scientific article