@article{Cătinaş_2001, title={On accelerating the convergence of the successive approximations method}, volume={30}, url={https://ictp.acad.ro/jnaat/journal/article/view/2001-vol30-no1-art1}, DOI={10.33993/jnaat301-675}, abstractNote={<p>In a previous paper of us, we have shown that no q-superlinear&nbsp;convergence to a fixed point \(x^\ast\) of a nonlinear mapping \(G\)&nbsp;may be attained by the successive approximations when \(G^\prime(x^\ast)\) has no eigenvalue equal to 0.&nbsp;However, high convergence orders may be attained if one considers&nbsp;perturbed successive approximations.<br>We characterize the correction terms which must be added at each step&nbsp;in order to obtain convergence with q-order 2 of the resulted&nbsp;iterates.</p>}, number={1}, journal={Rev. Anal. Numér. Théor. Approx.}, author={Cătinaş, Emil}, year={2001}, month={Feb.}, pages={3–8} }