| Title:
|
On an application of a Newton-like method to the approximation of implicit functions (English) |
| Author:
|
Argyros, Ioannis K. |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
42 |
| Issue:
|
3 |
| Year:
|
1992 |
| Pages:
|
339-347 |
| . |
| Category:
|
math |
| . |
| MSC:
|
46G05 |
| MSC:
|
47J25 |
| MSC:
|
47L05 |
| MSC:
|
65J15 |
| idZBL:
|
Zbl 0771.47035 |
| idMR:
|
MR1182964 |
| . |
| Date available:
|
2009-09-25T10:40:08Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/132917 |
| . |
| Reference:
|
[1] ARGYROS I. K : Newton-like methods under mild differentiability conditions with error analysis.Bull. Austral. Math. Soc. 37 (1987), 131-147. MR 0926985 |
| Reference:
|
[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 0261778 |
| Reference:
|
[3] CHEN X., YAMAMOTO T.: Convergence domains of certain iterative methods for solving nonlinear equations.Numer. Funct. Anal. Optim. 10 (1989), 37-48. Zbl 0645.65028, MR 0978801 |
| Reference:
|
[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. Zbl 0276.65029, MR 0278556 |
| Reference:
|
[5] KANTOROVICH L. V., AKILOV G. P.: Functional Analysis in Normed Spaces.Pergamon Press, New York, 1964. Zbl 0127.06104, MR 0213845 |
| Reference:
|
[6] KRASNOLESKII M. A., VAINIKKO G. M., ZABREJKO P. P., al.: The Approximate Solution of Operator Equations.(Russian), Nauka, Moscow, 1969. MR 0259635 |
| Reference:
|
[7] POTRA F. A., PTÁK V.: Sharp error bounds for Newton's process.Numer. Math. 34 (1980), 63-72. Zbl 0434.65034, MR 0560794 |
| Reference:
|
[8] RALL L. B.: A note on the convergence theory of Newton's method.SIAM J. Numer. Anal. 1 (1974), 34-36. MR 0343599 |
| Reference:
|
[9] RHEINBOLDT W. C.: A unified convergence theory for a class of iterative processes.SIAM J. Numer. Anal. 5 (1968), 42-63. Zbl 0155.46701, MR 0225468 |
| Reference:
|
[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. Zbl 0378.65029, MR 0514377 |
| Reference:
|
[11] YAMAMOTO T.: A convergence theorem for Newton-like methods in Banach spaces.Numer. Math. 51 (1987), 545-557. Zbl 0633.65049, MR 0910864 |
| Reference:
|
[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. Zbl 0627.65069, MR 0895991 |
| Reference:
|
[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 0160096 |
| . |
