New higher-order methods for the simultaneous inclusion of polynomial zeros |
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Authors: | Miodrag S Petković Mimica R Milošević Dušan M Milošević |
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Institution: | 1.Faculty of Electronic Engineering, Department of Mathematics,University of Ni?,Ni?,Serbia;2.Faculty of Science, Department of Mathematics,University of Ni?,Ni?,Serbia |
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Abstract: | Higher-order methods for the simultaneous inclusion of complex zeros of algebraic polynomials are presented in parallel (total-step)
and serial (single-step) versions. If the multiplicities of each zeros are given in advance, the proposed methods can be extended
for multiple zeros using appropriate corrections. These methods are constructed on the basis of the zero-relation of Gargantini’s
type, the inclusion isotonicity property and suitable corrections that appear in two-point methods of the fourth order for
solving nonlinear equations. It is proved that the order of convergence of the proposed methods is at least six. The computational
efficiency of the new methods is very high since the acceleration of convergence order from 3 (basic methods) to 6 (new methods)
is attained using only n polynomial evaluations per iteration. Computational efficiency of the considered methods is studied in detail and two numerical
examples are given to demonstrate the convergence behavior of the proposed methods. |
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