Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1139020 | Mathematics and Computers in Simulation | 2016 | 10 Pages |
Abstract
We present a new convergence analysis, for the secant method in order to approximate a locally unique solution of a nonlinear equation in a Banach space. Our idea uses Lipschitz and center–Lipschitz instead of just Lipschitz conditions in the convergence analysis. The new convergence analysis leads to more precise error bounds and to a better information on the location of the solution than the corresponding ones in earlier studies. Numerical examples validating the theoretical results are also provided in this study.
Related Topics
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Authors
Á. Alberto Magreñán, Ioannis K. Argyros,