Semilocal Convergence and Its Computational Efficiency of a Seventh-Order Method in Banach Spaces
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The present paper describes the study of semilocal convergence of seventh-order iterative method, in Banach spaces for solving nonlinear equations. The existence and uniqueness results have been verified followed by error bounds. It is also discussed that the considered scheme has not only the higher convergence order but also improved computational efficiency, which is the significant issue when dealing the nonlinear system problems. The theoretical development has been justified by applying it to a numerical problem.
KeywordsBanach space Local convergence Semilocal convergence Computational efficiency Error bound
Mathematics Subject Classification65J15 65H10 65G99 47J25
This work is supported by Science and Engineering Research Board (SERB), New Delhi, India under the scheme Start-up-Grant (Young Scientists) (Ref. No. YSS/2015/001507).