Abstract:In this paper, several one-parameter families of root-finding algorithms that have higher order convergence to simple and/or multiple roots have been derived. Specifically, the rth root iterations for simple and multiple zeros are analyzed. The rth root iteration family is an infinite family of rth order methods for every positive integer r, and uses only the first r − 1 derivatives. This family includes Newton's method and the square root iteration as the first and second member, respectively. In addition, th… Show more
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