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- W2277238161 abstract "The objective of this paper is to define a new Newton-type method for finding simple roots of nonlinear equations. It is proved that the new method has the convergence order of three requiring only two function evaluations per iteration. Kung and Traub conjectured that the multipoint iteration methods, without memory based on n evaluations, could achieve maximum convergence order 1 2 n− , but the new method produces convergence order of three, which is better than expected maximum convergence order of two. Therefore, we show that the conjecture fails for a particular set of nonlinear equations. In fact, we have found that the new method is only usable for zero roots. However, it is observed that our proposed method is very competitive with the third-order methods, thus the new method is very effective in high precision computations." @default.
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- W2277238161 date "2016-01-01" @default.
- W2277238161 modified "2023-09-26" @default.
- W2277238161 title "New Modification of Newton Method with Third-Order Convergence for Solving Nonlinear Equations of Type f (0)=0" @default.
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