Comparative study of methods of various orders for finding simple roots of nonlinear equations
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Recently there were many papers discussing the basins of attraction of various methods and ideas how to choose the parameters appearing in families of methods and weight functions used. Here we collected many of the results scattered and put a quantitative comparison of methods of orders from 2 to 7. We have used the average number of function-evaluations per point, the CPU time and the number of black points to compare the methods. We also include the best eighth order method. Based on 7 examples, we show that there is no method that is best based on the 3 criteria. We found that the best eighth order method, SA8, and CLND are at the top.
The article of record as published may be found at http://dx.doi.org/10.1007/s11075-016-0191-y
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