论文信息 - Chebyshev method and convexity

Chebyshev method and convexity

From convexity we obtain new convergence theorems for the Chebyshev method applied to a nonlinear scalar equation f(x) = 0. Moreover, Kantorovich type conditions for the convergence of the Chebyshev method in the complex plane are given. Finally, a new type of assumptions are considered to prove the convergence of this method in Banach spaces.

Miguel Ángel Hernández | M. A. Salanova | M. Hernández

[1] A. Householder. The numerical treatment of a single nonlinear equation , 1970 .

[2] Huang Zhengda. A note on the Kantorovich theorem for Newton iteration , 1993 .

[3] Ioannis K. Argyros,et al. Results on the Chebyshev method in banach spaces , 1993 .

[4] W. Rheinboldt. A unified convergence theory for a class of iterative processes. , 1968 .

[5] Miguel Angel Hernández Verón,et al. A note on Halley's method , 1991 .

[6] Miguel Ángel Hernández,et al. Accessibility Of Solutions By Newton's Method , 1995, Int. J. Comput. Math..

[7] Jon G. Rokne,et al. Newton's method under mild differentiability conditions with error analysis , 1971 .

[8] A. Ostrowski. Solution of equations and systems of equations , 1967 .

[9] Tetsuro Yamamoto,et al. On the method of tangent hyperbolas on Banach spaces , 1988 .