Convergence analysis for the Secant method based on new recurrence relations |
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| Authors: | Wei-hong Bi Hong-min Ren Qing-biao Wu |
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| Institution: | [1]Department of Mathematics, Zhejiang University, Hangzhou 310027, China [2]College of Information and Engineering, Hangzhou Radio and TV University, Hangzhou 310012,China |
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| Abstract: | A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation.It is assumed that the divided difference of order one of the nonlinear operator is Lipschitz continuous.The convergence conditions differ from some existing ones and are easily satisfied.The results of the paper are justified by numerical examples that cannot be handled by earlier works. |
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| Keywords: | Secant method Banach space recurrence relation semilocal convergence Lipschitz continuous divided difference |
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