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T. Lotfi, K. Mahdidni, "A New 'With' Memory Method using Two Accelerators", in , (Editors), "Proceedings of the Ninth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 37, 2014. doi:10.4203/ccp.105.37

Keywords: nonlinear equations, iterative methods, multipoint methods, without memory methods, with memory methods, Kung and Traub's conjecture, efficiency index.

Summary

In this work, we attempt to develop a new and efficient two-point with memory method to estimate simple roots of a given nonlinear equation. To this end, first, we consider an optimal two-point method without memory in which it uses only three functional evaluations per iteration having convergence order four. Applying two accelerator parameters in each iteration, we try to increase the convergence order from four to seven without any new extra function evaluations. We call it with memory method. Consequently, the efficiency index of the optimal two-point without memory method is increased from 4^1/3~1.58 to 7^1/3~1.91 which is better than an optimal five-step (or six-point) without memory with efficiency index equal to 32^1/6~1.78

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 105 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: Paper 37 A New 'With' Memory Method using Two Accelerators T. Lotfi and K. Mahdidni Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran doi:10.4203/ccp.105.37 purchase the full-text of this paper Full Bibliographic Reference for this paper T. Lotfi, K. Mahdidni, "A New 'With' Memory Method using Two Accelerators", in , (Editors), "Proceedings of the Ninth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 37, 2014. doi:10.4203/ccp.105.37 Keywords: nonlinear equations, iterative methods, multipoint methods, without memory methods, with memory methods, Kung and Traub's conjecture, efficiency index. Summary In this work, we attempt to develop a new and efficient two-point with memory method to estimate simple roots of a given nonlinear equation. To this end, first, we consider an optimal two-point method without memory in which it uses only three functional evaluations per iteration having convergence order four. Applying two accelerator parameters in each iteration, we try to increase the convergence order from four to seven without any new extra function evaluations. We call it with memory method. Consequently, the efficiency index of the optimal two-point without memory method is increased from 4^1/3~1.58 to 7^1/3~1.91 which is better than an optimal five-step (or six-point) without memory with efficiency index equal to 32^1/6~1.78 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £45 +P&P)
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