Abstract: Let f:E→F be a Frrehet derivable map from one Banach space to anothet and A:F→E be a linear map with bounded inverse．We call the iteration Zn+l=Zn-A??(Zn)，VnE No，a generalized chlrd method iteration.When A=D?(Zo)-1，the iteration is the modified Newton m~hod iteration．The convergence an d convergence domain by recalls of Km-ropomm’s Domain criteria and Smale s point estinate criteria are studied．It contains a special case，the modified Newt on iteration convergence when α(f,z)<3-2√2．Thisdemonstratesthatnumber3-2√2 is universal for many concreteite rations．

摘要： Banach空间E的某个区域到同型空间的Fr~chet可微的算子f；E—F，A；F—E是一个相反的固定的线性 算子，迭代z=Z一Af(z)为简化牛顿迭代，其中Vn~NO，=，-(：0)一．用KatiTOPOBlttl的区域判据和Smale的点 估计判据研究广义简化牛顿迭代的收敛性和收敛域的大小，并且包括当口)-2√2时广义简化Newton迭代 收敛情况．

关键词: 优序列, 广义强迭代, 简化牛顿迭代