Estimates of Majorizing Sequences in the Newton–Kantorovich Method
Estimates of Majorizing Sequences in the Newton–Kantorovich Method
复制标题
牛顿-康托罗维奇方法中主化序列的估计
DOI：
10.1080/01630560600790793
复制
发表时间：
2006
影响因子：
1.2
通讯作者：
Espedito De Pascale
中科院分区：
文献类型：
--
作者：
F. Cianciaruso;Espedito De Pascale
设f：B（x 0，R）<$X → Y是一个算子，X和Y是Banach空间，f′是指数为θ的Hölder连续. Newton-Kantorovich逼近序列的收敛性是求解方程f（x）= 0的经典工具。xn的收敛性问题通常归结为对定义为a，B，k参数与f和f′有关的优化序列rn的研究。我们延长估计r n，已知在Lipschitz的情况下，Hölder的情况下。证明需要引入一个乘法因子的序列估计r n，估计的比率，并使用两个平行的感应过程的序列r n和。在最后一节中，我们与我们以前的结果进行了比较。
Let f:B(x 0,R) ⊆ X → Y be an operator, with X and Y Banach spaces, and f′ be Hölder continuous with exponent θ. The convergence of the sequence of Newton–Kantorovich approximations is a classical tool to solve the equation f(x) = 0. The convergence of x n is often reduced to the study of the majorizing sequence r n defined by with a, b, k parameters related to f and f′. We extend an estimate for r n , known in the Lipschitz case, to the Hölder case. The proof requires the introduction of a multiplicative factor in the sequence estimating r n , estimates of the ratio , and the use of two parallel induction processes on the sequences r n and . In the last section, we make a comparison with our previous results.