Some New Variants of Cauchy's Methods for Solving Nonlinear Equations
We present and analyze some variants of Cauchy's methods free from second derivative for obtaining simple roots of nonlinear equations. The convergence analysis of the methods is discussed. It is established that the methods have convergence order three. Per iteration the new methods require tw...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/927450 |
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| Summary: | We present and analyze some variants of Cauchy's methods free from
second derivative for obtaining simple roots of nonlinear equations. The convergence
analysis of the methods is discussed. It is established that the methods have convergence order three. Per iteration the new methods require two function and one first
derivative evaluations. Numerical examples show that the new methods are comparable with the well-known existing methods and give better numerical results in many
aspects. |
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| ISSN: | 1110-757X 1687-0042 |