On a modification of Chebyshev's method

AbstractA new iterative method for finding simultaneously all zeros of generalized polynomials is considered in this paper. The method is based on the classical Chebyshev's method for finding individually roots of nonlinear equations. Two numerical experiments are presented, where the new method gives better results than Chebyshev's method, but the inverse case is also impossible. The main idea in this paper however is to show the close connection between the classical methods (for individual finding) and the methods for finding simultaneously zeros of polynomials. Here we remind that the famous method of Ehrlich (1967) can be obtained from the classical Obreshkov's (1958, 1963) and Heinz's (1963) method applying the technique described below