On the local convergence of fast two-step Newton-like methods for solving nonlinear equations
A local convergence analysis is presented for a fast two-step Newton-like method (TSNLM) for solving nonlinear equations in a Banach space setting. The TSNLM unifies earlier methods such as Newton’s, Secant, Newton-like, Chebyshev–Secant, Chebyshev–Newton, Steffensen, Stirling’s and other single or...
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| Published in: | Journal of computational and applied mathematics Vol. 245; pp. 1 - 9 |
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| Format: | Journal Article |
| Language: | English |
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01-06-2013
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| Abstract | A local convergence analysis is presented for a fast two-step Newton-like method (TSNLM) for solving nonlinear equations in a Banach space setting. The TSNLM unifies earlier methods such as Newton’s, Secant, Newton-like, Chebyshev–Secant, Chebyshev–Newton, Steffensen, Stirling’s and other single or multistep methods. Numerical examples and a comparative study of these methods validating our theoretical results are also given in the concluding section of this paper. |
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| AbstractList | A local convergence analysis is presented for a fast two-step Newton-like method (TSNLM) for solving nonlinear equations in a Banach space setting. The TSNLM unifies earlier methods such as Newton's, Secant, Newton-like, Chebyshev-Secant, Chebyshev-Newton, Steffensen, Stirling's and other single or multistep methods. Numerical examples and a comparative study of these methods validating our theoretical results are also given in the concluding section of this paper. |
| Author | Hilout, S. Argyros, I.K. |
| Author_xml | – sequence: 1 givenname: I.K. surname: Argyros fullname: Argyros, I.K. email: iargyros@cameron.edu organization: Cameron University, Department of Mathematical Sciences, Lawton, OK 73505, USA – sequence: 2 givenname: S. surname: Hilout fullname: Hilout, S. email: said.hilout@math.univ-poitiers.fr organization: Poitiers University, Laboratoire de Mathématiques et Applications, 86962 Futuroscope Chasseneuil Cedex, France |
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Math. doi: 10.1007/BF01397473 contributor: fullname: Wolfe – volume: 235 start-page: 3195 year: 2011 ident: 10.1016/j.cam.2012.12.002_br000040 article-title: On the semilocal convergence of efficient Chebyshev–Secant-type methods publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2011.01.005 contributor: fullname: Argyros – volume: 4 start-page: 156 year: 1969 ident: 10.1016/j.cam.2012.12.002_br000050 article-title: A multipoint method of third order publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00930576 contributor: fullname: Bosarge – volume: 55 start-page: 175 year: 2005 ident: 10.1016/j.cam.2012.12.002_br000080 article-title: New sufficient convergence conditions for the Secant method publication-title: Chechoslovak Math. J. doi: 10.1007/s10587-005-0013-1 contributor: fullname: Argyros – volume: 17 start-page: 509 year: 2004 ident: 10.1016/j.cam.2012.12.002_br000035 article-title: A variant of Cauchy’s method with accelerated fifth-order convergence publication-title: Appl. Math. Lett. doi: 10.1016/S0893-9659(04)90119-X contributor: fullname: Grau |
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| Snippet | A local convergence analysis is presented for a fast two-step Newton-like method (TSNLM) for solving nonlinear equations in a Banach space setting. The TSNLM... |
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| SubjectTerms | Banach space Chebyshev approximation Chebyshev’s method Computation Convergence Mathematical models Newton methods Newton-like method Newton’s method Nonlinear equations Secant method Semilocal convergence |
| Title | On the local convergence of fast two-step Newton-like methods for solving nonlinear equations |
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