Inexact perturbed Newton methods and applications to a class of Krylov solvers
Abstract Inexact Newton methods are variant of the Newton method in which each step satisfies only approximately the linear system…
2001
On accelerating the convergence of the successive approximations method
Abstract No q-superlinear convergence to a fixed point \(x^\ast\) of a nonlinear mapping \(G\) may be attained by the successive approximations when…
A Halley-Aitken-type method for approximating the solutions of scalar equations
Abstract We are concerned with the approximation of the solution of scalar equations by Halley-Aitken method. We obtain local convergence…
On some Aitken-Steffensen-Halley-type method for approximating the roots of scalar equations
Abstract We extend the Aitken-Steffensen method to the Halley transformation. Under some rather simple assumptions we obtain error bounds for…
On a Halley-Steffensen method for approximating the solutions of scalar equations
Abstract We show that the Steffensen method for solving the scalar equation \(f(x)=0\), applied to equation $$h(x)=\frac{f(x)}{\sqrt{f'(x)}}=0,$$ leads to bilateral…