On the discretization of newton-like methods

References

• Allgower , E. L. , Bohmer , K. , Potra , F. A. and Rheinboldt , W. C. 1986 . A mesh-independence principle for operator equations and their discretizations . S.I A.M. J. Num. Anal. , 23 ( 1 ) : 160 – 169 .
   Web of Science ®Google Scholar
• Argyros , I. K. 1987 . Newton-like method methods under mild differentiability conditions with eror analysis . Bull. Austral. Math. Soc. , 37 ( 2 ) : 131 – 147 .
   Google Scholar
• Dennis , J. E. 1971 . “ Toward a unified convergence theory for Newton-like methods Nonlinear functional analysis and applications ” . Edited by: Rall , L. B. New York : Academic Press .
   Google Scholar
• Kantorovich , L. V. and Akilov , G. P. 1964 . Functional Analysis in Normed Spaces , Oxford: Pergamon Press .
   Google Scholar
• Kornstaedt , H. J. 1975 . Functional Ungleichugen und Iterationsverfahren . Aequat. Math , 13 : 21 – 45 .
   Google Scholar
• Mc Cormick , S. F. 1978 . “ A revised mesh refinement strategy for Newton's method applied to two-point boundary value problems ” . In Lecture Notes in Mathematics , Vol. 674 , Berlin : Springer-Verlag .
   Google Scholar
• Ptak , V. 1976 . Nondiscrete mathematical induction and existence proofs . Linear Algebra Appl , 13 : 223 – 236 .
   Web of Science ®Google Scholar
• Rheinboldt , W. C. 1977 . An adaptive continuation process for solving systems of nonlinear equations . Polish Academy of Sciences Banach Crt. Publ , 3 : 129 – 142 .
   Google Scholar
• Schmidt , J. W. 1978 . Under Fehrerschranken fur Regular-falsi-Verfahren . Period. Math. Hung , 9 : 241 – 247 .
   Google Scholar
• Yamamoto , T. 1987 . A convergence theorem for Newton-like methods in Banach spaces . Numer. Math. , 51 : 545 – 557 .
   Web of Science ®Google Scholar
• Vainikko , G. M. 1967 . Galerkin's pertubation method and the general theory of a approximate methods for non-linear equations . U.S.S.R. Comp. Math, and Math. Phys. , 4 : 723 – 751 .
   Google Scholar