A high-order iterative formula for simultaneous determination of zeros of a polynomial
Copyright policy )A high-order iterative formula for simultaneous determination of zeros of a polynomial
The authors introduce two algorithms (simultaneous formulae by the Padé approximation and a hybrid method, respectively) to determine all zeros of a polynomial with complex coefficients, and present three examples with three tables of the numerical results. By the end the authors give explicit formulae of the algorithms for the methods of \textit{M. R. Farmer} and \textit{G. Loizou} [BIT, Nordisk Tidskr. Inform.-behandl. 15, 250-258 (1975; Zbl 0311.65036)] and of \textit{X. Wang} and \textit{S. Zheng} [J. Comput. Math. 2, 70-76 (1984; Zbl 0541.65028)] in the case of order \(m=2\).
simultaneous iterative method, high-order iterative formula, multiple roots, Applied Mathematics, numerical results, algorithms, single-root method, Computational Mathematics, zeros of a complex polynomial, polynomial equation, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), root finding algorithm, Numerical computation of solutions to single equations, high convergence order, Padé approximation, Root finding algorithm
simultaneous iterative method, high-order iterative formula, multiple roots, Applied Mathematics, numerical results, algorithms, single-root method, Computational Mathematics, zeros of a complex polynomial, polynomial equation, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), root finding algorithm, Numerical computation of solutions to single equations, high convergence order, Padé approximation, Root finding algorithm
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