High order iterative methods for approximating square roots
The authors describe an iteration function \(g_m(x)\) with \(m\geq 2\) having the propriety that for any initial iterate \(x_0> \sqrt \alpha\), the sequence of fixed-point iteration \(x_{k+1} =g_m (x_k)\) converges monotonically to \(\sqrt \alpha\) having \(m\)-th order rate of convergence. This function generalizes Newton's and Halley's iteration functions.
Newton's and Halley's iteration functions
scientific article; zbMATH DE number 885561