FAMILY OF SIMULTANEOUS METHODS WITH CORRECTIONS FOR APPROXIMATING ZEROS OF ANALYTIC FUNCTIONS
Abstract
A family of accelerated iterative methods for the
simultaneous approximation 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. It is shown that the order of convergence of the basic
family can be increased from four to five
and six using Newton's and Halley's
corrections, respectively. The improved convergence is achieved
on the account of additional calculations of low computational cost, which
significantly increases the computational efficiency of the
accelerated methods. Numerical examples demonstrate a good
convergence properties, fitting very well theoretical results.
simultaneous approximation 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. It is shown that the order of convergence of the basic
family can be increased from four to five
and six using Newton's and Halley's
corrections, respectively. The improved convergence is achieved
on the account of additional calculations of low computational cost, which
significantly increases the computational efficiency of the
accelerated methods. Numerical examples demonstrate a good
convergence properties, fitting very well theoretical results.
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