IMPROVED HIGHER ORDER METHOD FOR THE INCLUSION OF MULTIPLE ZEROS OF POLYNOMIALS

Starting from a suitable fixed point relation and employing Schroder's and Halley-like corrections, wederive some high order iterative methods for the simultaneous inclusion of polynomial multiple zeros in circular complex interval arithmetic. These methods are more efficient compared to the existing inclusion methods based on fixed point relations. Using the concept of the R-order of convergence of mutually dependent sequences, we present the convergence analysis of the obtained total-step and single-step methods. The proposed self-validated methods possess a great computational efficiency since the acceleration of the convergence rate from four to seven is achieved with only few additional calculations. Numerical examples illustrate the convergence properties of the presented methods.