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- Title
Chebyshev-like root-finding methods with accelerated convergence.
- Authors
Petković, M. S.; Rančić, L.; Petković, L. D.; Ilić, S.
- Abstract
Iterative methods for the simultaneous determination of simple or multiple complex zeros of a polynomial, based on a cubically convergent Chebyshev method, are considered. Using Newton's and Halley's corrections the convergence of the basic method of the fourth order is increased to five and six, respectively. The improved convergence is achieved with negligible number of additional calculations, which significantly increases the computational efficiency of the accelerated methods. One of the most important problems in solving polynomial equations, the construction of initial conditions that enable both guaranteed and fast convergence, is also studied for the proposed methods. These conditions are computationally verifiable since they depend only on initial approximations, the polynomial coefficients and the polynomial degree, which is of practical importance. Finally, modified methods of Chebyshev's type for finding multiple zeros and single-step methods based on the Gauss–Seidel approach are constructed. Copyright © 2009 John Wiley & Sons, Ltd.
- Subjects
ITERATIVE methods (Mathematics); CHEBYSHEV polynomials; ZERO (The number); ACCELERATION of convergence in numerical analysis; APPROXIMATION theory
- Publication
Numerical Linear Algebra with Applications, 2009, Vol 16, Issue 11/12, p971
- ISSN
1070-5325
- Publication type
Article
- DOI
10.1002/nla.661