@article{MASLO_1992_42_3_a9,
author = {Argyros, Ioannis K.},
title = {On an application of a {Newton-like} method to the approximation of implicit functions},
journal = {Mathematica slovaca},
pages = {339--347},
year = {1992},
volume = {42},
number = {3},
mrnumber = {1182964},
zbl = {0771.47035},
language = {en},
url = {http://geodesic.mathdoc.fr/item/MASLO_1992_42_3_a9/}
}
Argyros, Ioannis K. On an application of a Newton-like method to the approximation of implicit functions. Mathematica slovaca, Tome 42 (1992) no. 3, pp. 339-347. http://geodesic.mathdoc.fr/item/MASLO_1992_42_3_a9/
[1] ARGYROS I. K : Newton-like methods under mild differentiability conditions with error analysis. Bull. Austral. Math. Soc. 37 (1987), 131-147. | MR
[2] BALAZS, M, GOLDNER G.: On the method of the cord and on a modification of it for the solution of nonlinear operator equations. Stud. Cere. Mat. 20 (1968), 981-990. | MR
[3] CHEN X., YAMAMOTO T.: Convergence domains of certain iterative methods for solving nonlinear equations. Numer. Funct. Anal. Optim. 10 (1989), 37-48. | MR | Zbl
[4] DENNIS J. E.: Toward a unified convergence theory for Newton-like methods. In: Nonlinear Functional Analysis and Applications (L. B. Rail, ed.), Academic Press, New York, 1971, pp. 425-472. | MR | Zbl
[5] KANTOROVICH L. V., AKILOV G. P.: Functional Analysis in Normed Spaces. Pergamon Press, New York, 1964. | MR | Zbl
[6] KRASNOLESKII M. A., VAINIKKO G. M., ZABREJKO P. P., al.: The Approximate Solution of Operator Equations. (Russian), Nauka, Moscow, 1969. | MR
[7] POTRA F. A., PTÁK V.: Sharp error bounds for Newton's process. Numer. Math. 34 (1980), 63-72. | MR | Zbl
[8] RALL L. B.: A note on the convergence theory of Newton's method. SIAM J. Numer. Anal. 1 (1974), 34-36. | MR
[9] RHEINBOLDT W. C.: A unified convergence theory for a class of iterative processes. SIAM J. Numer. Anal. 5 (1968), 42-63. | MR | Zbl
[10] RHEINBOLDT W. C.: An adaptive continuation process for solving systems of nonlinear equations. In: Mathematical Models and Numerical Methods. (A. N. Tikhonov and others, eds.) Banach Center Publications 3, PWN-Polish Scientific Publishers, Warszawa, 1978, pp. 129-142. | MR | Zbl
[11] YAMAMOTO T.: A convergence theorem for Newton-like methods in Banach spaces. Numer. Math. 51 (1987), 545-557. | MR | Zbl
[12] ZABREJKO P. P., NGUEN D. F.: The majorant method in the theory of Newton-Kantorovich approximations and the Pták error estimates. Numer. Funct. Anal. Optim. 9 (1987), 671-684. | MR | Zbl
[13] ZINCENKO A. I.: Some approximate methods of solving equations with nondifferentiable operators. (Ukrainian), Dopovïdï Akad. Nauk Ukraïn. RSR Ser. A (1963), 156-161. | MR