Abstract.
In this paper we present iteration methods of Halley's type for the simultaneous inclusion of all zeros of a polynomial. Using the concept of the R-order of convergence of mutually dependent sequences, we present the convergence analysis for the total-step and the single-step methods with Newton's corrections. The suggested algorithms possess a great computational efficiency since the increase of the convergence rate is attained without additional calculations. A numerical example is given.
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Received: June 23, 1998
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Petković, M. Halley-Like Method with Corrections for the Inclusion of Polynomial Zeros. Computing 62, 69–88 (1999). https://doi.org/10.1007/s006070050014
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DOI: https://doi.org/10.1007/s006070050014