Generalized quasilinearization versus Newton method (Q556065)

The authors compare the classical Newton method for finding roots of a single algebraic equation of the form \(f(x)=0\) to quasilinearization methods with a view to bracket the root of the nonlinear algebraic equation in intervals of decreasing lengths, which converge quadratically on the root. The applicability of the approach requires the existence of \(f_{xx}\) in the respective intervals.