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Local convergence results for three Newton-like methods in Banach
space are provided. A comparison is given between the three convergence radii.
Then we show that using the largest convergence radius we can pick an initial guess
from with we start the corresponding iteration. It turns out that after a ¯nite
number of steps we can always use the iterate found as the starting guess for a
faster method, since this iterate will be inside the convergence domain of the new
method.
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참고문헌 (9)
참고문헌 신청
Argyros, I. K. / 2004 / A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space / J. Math. Anal. Appl 298 (2) : 374
Argyros, I.K. / 2005 / Approximate solution of operator equations with applications / World Scientic Publ. Co.
Chen, X. / 1989 / Convergence domains of certain iterative methods for solving nonlinear equations / Numer. Funct. Anal. Optim 10 : 37 ~ 48
Deuflhard, P. / 1979 / Affine invariant convergence theorems for Newton's method and extensions to related methods / SIAM J. Numer. Anal 16 : 1 ~ 10
Gutierrez, J.M. / 1995 / Accessibilty of solutions by Newton's method 57 : 239 ~ 247
Argyros, I.K. / 2005 / Approximate solution of operator equations with applications / World Scientic Publ. Co.
Chen, X. / 1989 / Convergence domains of certain iterative methods for solving nonlinear equations / Numer. Funct. Anal. Optim 10 : 37 ~ 48
Deuflhard, P. / 1979 / Affine invariant convergence theorems for Newton's method and extensions to related methods / SIAM J. Numer. Anal 16 : 1 ~ 10
Gutierrez, J.M. / 1995 / Accessibilty of solutions by Newton's method 57 : 239 ~ 247
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