一类变异型Chebyshev-Halley迭代法的收敛性

Convergence of the variants of a Chebyshev-Halley iteration family

研究了一类变异型Chebyshev-Halley迭代法的收敛性.给出了在满足条件‖F"(x)‖≤ω(‖x‖)时的迭代法收敛性判据及半局部收敛性的证明,最后分析了参数α的变化对收敛半径的影响,以期为某种参数的选择提供依据.

Under condition ‖F＇＇（ x）‖≤ω（‖x‖） , the convergence of the variants of a Chebyshev-Halley iteration family was discussed. The convergence criterion and semi-local convergence were obtained. The impact of the change of parameter α on the convergence radius was analyzed, so a kind of choosing criterion for parameters was provided.