The Improved Square-root Methods for the Inclusion of Multiple Zeros of Polynomials
نویسندگان
چکیده
Starting from a fixed point relation, we construct very fast iterative methods of Ostrowski-root’s type for the simultaneous inclusion of all multiple zeros of a polynomial. The proposed methods possess a great computational efficiency since the acceleration of the convergence is attained with only a few additional calculations. Using the concept of the R-order of convergence of mutually dependent sequences, we present the convergence analysis of the total-step method with Schröder’s and Halley’s corrections under computationally verifiable initial conditions. Further acceleration is attained by the Gauss-Seidel approach (single-step mode). Numerical examples are given to demonstrate properties of the proposed inclusion methods. AMS Mathematics Subject Classification (2000): 65H05, 65G20, 30C15
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تاریخ انتشار 2010