Relationships between different types of initial conditions for simultaneous root finding methods |
| |
Institution: | Faculty of Mathematics and Informatics, University of Plovdiv, Plovdiv 4000, Bulgaria |
| |
Abstract: | The construction of initial conditions of an iterative method is one of the most important problems in solving nonlinear equations. In this paper, we obtain relationships between different types of initial conditions that guarantee the convergence of iterative methods for simultaneously finding all zeros of a polynomial. In particular, we show that any local convergence theorem for a simultaneous method can be converted into a convergence theorem with computationally verifiable initial conditions which is of practical importance. Thus, we propose a new approach for obtaining semilocal convergence results for simultaneous methods via local convergence results. |
| |
Keywords: | Iterative methods Simultaneous methods Initial conditions Polynomial zeros Local convergence Semilocal convergence |
本文献已被 ScienceDirect 等数据库收录! |