Majorizing sequences and error bounds for iterative methods
Majorizing sequences and error bounds for iterative methods
复制标题
迭代方法的主要序列和误差范围
DOI：
10.1090/s0025-5718-1980-0551297-4
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发表时间：
1980
影响因子：
2
通讯作者：
G. Miel
中科院分区：
文献类型：
--
作者：
G. Miel
给定Banach空间中的序列{xn}n= 0，如果存在序列{tn}n= 0使得llxn+ -xlx 6 tn+ tn且lim tn = t？n（tn nd 1xn@n1 t1 -o）给出了i = 1时xn = Gxn和Xn = H（xn，xn 1）型无穷级数和迭代的典型应用.在Kantorovich定理的假设下，证明了0 <，< 2的误差估计对于Newton迭代是有效的和最优的。利用Rheinboldt的统一收敛理论，得到了一类Nbwton型方法在0 <，< 1时的误差界，并证明了这些误差界对于一类方法是最优的.的误差范围的实际限制进行了说明。
Given a sequence {xn}n=o in a Banach space, it is well known that if there is a sequence {tn}n=O such that llxn+ -xlx 6 tn+ tn and lim tn = t ?n (tn nd 1xn @ n1 t1 -o Representative applications to infinite series and to iterates of types xn = Gxn and Xn = H(xn, xn1) are given for i = 1. Error estimates with 0 < , < 2 are shown to be valid and optimal for Newton iterates under the hypotheses of the Kantorovich theorem. The unified convergence theory of Rheinboldt is used to derive error bounds with 0 < , < 1 for a class of Nbwton-type methods, and these bounds are shown to be optimal for a subclass of methods. Practical limitations of the error bounds are described.