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A  family of iterative methods for the simultaneous determination of complex zeros of a class of analytic functions, is proposed. Considered  analytic functions  have only simple zeros inside a simple smooth closed contour in the complex plane. We  show that the convergence of the basic family of the fourth order can be increased to five and six using Newton's and Halley's corrections, respectively. The improved convergence is achieved with negligible number of additional calculations, which significantly increases the computational efficiency of the accelerated methods.  Numerical example demonstrate a good convergence properties, fitting very well theoretical results.

Family of iterative methods, simultaneous methods, zeros of analytic functions, convergence.