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High order Euler-like method for the inclusion of polynomial zeros

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Volume
196
Issue
2
Identifiers
DOI: 10.1016/j.amc.2007.07.007
Keywords
  • Zeros Of Polynomials
  • Complex Zeros
  • Simultaneous Methods
  • Inclusion Methods
  • Error Bounds
  • Circular Interval Arithmetic
  • Convergence
Disciplines
  • Computer Science

Abstract

Abstract Improved iterative method of Euler’s type for the simultaneous inclusion of polynomial zeros is considered. To accelerate the convergence of the basic method of the fourth order we applied Börsch–Supan’s correction. It is proved that the R-order of convergence of the improved Euler-like method is six. The convergence analysis is derived under computationally verifiable initial conditions. The proposed algorithm possesses great computational efficiency since the increase of the convergence rate from 4 to 6 is obtained with negligible number of additional calculations. In order to demonstrate convergence properties of the suggested method, two numerical examples are given.

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