Unified error analysis for Newton-type methods

An error analysis for the secant method

“…The results obtained in the perturbed case are new. Similar results concerning Newton's process can be found in the papers of P. Lancaster [2], J. Rokne [14] and G. Miel [3].…”

A convergence theorem for Newton-like methods in Banach spaces

“…A further generalization was given by Dennis [4,5]. Miel [15,16] improved the error bounds for Rheinboldt [27]. Motet [18] obtained a convergence theorem as well as error bounds for the iteration (1.2) under the stronger conditions than those of Rheinboldt.…”

On the convergence of Newton-type methods under mild differentiability conditions

“…Using our new idea of recurrent functions, a combination of Lipschitz and center-Lipschitz conditions, instead of only Lipschitz conditions, we provided an analysis with the following advantages over the works in [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]: weaker sufficient convergence conditions, and larger convergence domain.…”