Mysovskii-type theorem for the Secant method under Hölder continuous Fréchet derivative |
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Authors: | Hongmin Ren Qingbiao Wu |
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Institution: | a Department of Information and Engineering, Hangzhou Radio and TV University, Hangzhou 310012, Zhejiang, PR China b Department of Mathematics, Zhejiang University, Hangzhou 310028, Zhejiang, PR China |
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Abstract: | The Mysovskii-type condition is considered in this study for the Secant method in Banach spaces to solve a nonlinear operator equation. We suppose the inverse of divided difference of order one is bounded and the Fréchet derivative of the nonlinear operator is Hölder continuous. By use of Fibonacci generalized sequence, a semilocal convergence theorem is established which matches with the convergence order of the method. Finally, two simple examples are provided to show that our results apply, where earlier ones fail. |
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Keywords: | The Secant method Semilocal convergence Mysovskii-type theorem Hö lder continuous Fré chet derivative |
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