统一判据下Chebyshev迭代的收敛性

Convergence Theorem for the Chebyshev' s Iteration in Banach Space

利用优函数研究了Banach空间中解非线性算子方程的Chebyshev迭代的的收敛性,建立了它的更为阔泛的Newton-Kantorovlch型收敛性定理,最后用例子说明了定理的应用．

By using majofizing function, we establish widely Kantorovich - type convergence theorem for the Chebyshev＇s method in Banach space. The theorem can be used to solve the nonlinear operator equation. Finally, two examples are provided to show the application of our theorem.