On an application of a Newton-like method to the approximation of implicit functions
Mathematica Slovaca (1992)
- Volume: 42, Issue: 3, page 339-347
- ISSN: 0139-9918
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topArgyros, Ioannis K.. "On an application of a Newton-like method to the approximation of implicit functions." Mathematica Slovaca 42.3 (1992): 339-347. <http://eudml.org/doc/32341>.
@article{Argyros1992,
author = {Argyros, Ioannis K.},
journal = {Mathematica Slovaca},
keywords = {Newton-like method to approximate implicit functions in a Banach space; error bounds},
language = {eng},
number = {3},
pages = {339-347},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {On an application of a Newton-like method to the approximation of implicit functions},
url = {http://eudml.org/doc/32341},
volume = {42},
year = {1992},
}
TY - JOUR
AU - Argyros, Ioannis K.
TI - On an application of a Newton-like method to the approximation of implicit functions
JO - Mathematica Slovaca
PY - 1992
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 42
IS - 3
SP - 339
EP - 347
LA - eng
KW - Newton-like method to approximate implicit functions in a Banach space; error bounds
UR - http://eudml.org/doc/32341
ER -
References
top- ARGYROS I. K, Newton-like methods under mild differentiability conditions with error analysis, Bull. Austral. Math. Soc. 37 (1987), 131-147. (1987) MR0926985
- 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. (1968) MR0261778
- CHEN X., YAMAMOTO T., Convergence domains of certain iterative methods for solving nonlinear equations, Numer. Funct. Anal. Optim. 10 (1989), 37-48. (1989) Zbl0645.65028MR0978801
- 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. (1971) Zbl0276.65029MR0278556
- KANTOROVICH L. V., AKILOV G. P., Functional Analysis in Normed Spaces, Pergamon Press, New York, 1964. (1964) Zbl0127.06104MR0213845
- KRASNOLESKII M. A., VAINIKKO G. M., ZABREJKO P. P., al., The Approximate Solution of Operator Equations, (Russian), Nauka, Moscow, 1969. (1969) MR0259635
- POTRA F. A., PTÁK V., Sharp error bounds for Newton's process, Numer. Math. 34 (1980), 63-72. (1980) Zbl0434.65034MR0560794
- RALL L. B., A note on the convergence theory of Newton's method, SIAM J. Numer. Anal. 1 (1974), 34-36. (1974) MR0343599
- RHEINBOLDT W. C., A unified convergence theory for a class of iterative processes, SIAM J. Numer. Anal. 5 (1968), 42-63. (1968) Zbl0155.46701MR0225468
- 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. (1978) Zbl0378.65029MR0514377
- YAMAMOTO T., A convergence theorem for Newton-like methods in Banach spaces, Numer. Math. 51 (1987), 545-557. (1987) Zbl0633.65049MR0910864
- 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. (1987) Zbl0627.65069MR0895991
- ZINCENKO A. I., Some approximate methods of solving equations with nondifferentiable operators, (Ukrainian), Dopovïdï Akad. Nauk Ukraïn. RSR Ser. A (1963), 156-161. (1963) MR0160096
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