Inaccuracy in quasi-Newton methods: Local improvement theorems
Inaccuracy in quasi-Newton methods: Local improvement theorems
复制标题
拟牛顿方法的不准确性：局部改进定理
DOI：
--
复制
发表时间：
1984
期刊：
影响因子：
--
通讯作者：
H. Walker
中科院分区：
文献类型：
--
作者：
J. Dennis;H. Walker
在本文中，我们考虑使用有界退化拟牛顿方法实现的浮点运算，以找到解决方案，F（x）=0，只有不准确的F值。我们的分析是针对F的相对误差小于1的情况。我们得到定理指定本地的改进率和限制精度取决于牛顿的方法的基本算法的接近度，其实施的准确性，在函数值的相对误差，牛顿步骤的线性系统的解决方案的准确性，和单位舍入误差中添加的牛顿步骤。
In this paper, we consider the use of bounded-deterioration quasi-Newton methods implemented in floating-point arithmetic to find solutions to F(x)=0 where only inaccurate F-values are available. Our analysis is for the case where the relative error in F is less than one. We obtain theorems specifying local rates of improvement and limiting accuracies depending on the nearness to Newton’s method of the basic algorithm, the accuracy of its implementation, the relative errors in the function values, the accuracy of the solutions of the linear system for the Newton steps, and the unit-rounding errors in the addition of the Newton steps.