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The principle aim of this manuscript is to introduce a new highly efficient improved modification of Chebyshev–Halley family with increasing order of convergence. The idea is based on the schemes proposed by Li et al. (Appl Math Comput 235:221–225, 2014) and Sharma (Appl Math Comput 256:119–124, 2015). The proposed scheme has at least seventh-order of convergence and also posses an optimal eighth-order...
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