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An optimal multiple root-finding method of order three. (English) Zbl 0814.65045
An optimal one-point iterative method of order three for determining a multiple zero of a complex function in a complex variable which requires less computational effort per iteration step than three known such optimal methods is presented. One numerical example with a non-real zero of multiplicity 5/2 is given.

MSC:
65H05 Numerical computation of solutions to single equations
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
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References:
[1] Hansen, T.; Patrick, M., A family of root finding methods, Numer. math., 27, 257-269, (1977) · Zbl 0361.65041
[2] Ostrowski, A.M., Solution of equations in Euclidean and Banach spaces, (1973), Academic Press New York · Zbl 0304.65002
[3] Traub, J.F., ()
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