On an application of a Newton-like method to the approximation of implicit functions

Ioannis K. Argyros

Mathematica Slovaca (1992)

  • Volume: 42, Issue: 3, page 339-347
  • ISSN: 0139-9918

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Argyros, 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

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  1. ARGYROS I. K, Newton-like methods under mild differentiability conditions with error analysis, Bull. Austral. Math. Soc. 37 (1987), 131-147. (1987) MR0926985
  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. (1968) MR0261778
  3. 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
  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. (1971) Zbl0276.65029MR0278556
  5. KANTOROVICH L. V., AKILOV G. P., Functional Analysis in Normed Spaces, Pergamon Press, New York, 1964. (1964) Zbl0127.06104MR0213845
  6. KRASNOLESKII M. A., VAINIKKO G. M., ZABREJKO P. P., al., The Approximate Solution of Operator Equations, (Russian), Nauka, Moscow, 1969. (1969) MR0259635
  7. POTRA F. A., PTÁK V., Sharp error bounds for Newton's process, Numer. Math. 34 (1980), 63-72. (1980) Zbl0434.65034MR0560794
  8. RALL L. B., A note on the convergence theory of Newton's method, SIAM J. Numer. Anal. 1 (1974), 34-36. (1974) MR0343599
  9. RHEINBOLDT W. C., A unified convergence theory for a class of iterative processes, SIAM J. Numer. Anal. 5 (1968), 42-63. (1968) Zbl0155.46701MR0225468
  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. (1978) Zbl0378.65029MR0514377
  11. YAMAMOTO T., A convergence theorem for Newton-like methods in Banach spaces, Numer. Math. 51 (1987), 545-557. (1987) Zbl0633.65049MR0910864
  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. (1987) Zbl0627.65069MR0895991
  13. 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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