Improved Higher Order Method for the Inclusion of Multiple Zeros of Polynomials∗
نویسندگان
چکیده
Starting from a suitable fixed point relation and employing Schröder’s and Halley-like corrections, we derive 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.
منابع مشابه
Higher Order Methods for the Inclusion of Multiple Zeros of Polynomials
Starting from a suitable fixed point relation, we derive higher order iterative methods for the simultaneous inclusion of polynomial multiple zeros in circular complex interval arithmetic. Each of the resulting disks contain one and only one zero in every iteration. This convenient inclusion property, together with very fast convergence, ranks these methods among the most powerful iterative met...
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