微机保护开平方计算中牛顿迭代法的改进

The Improvement of Newton Iteration Method in the Square Root Calculation of Microcomputer Protection

在分析了查表法以及牛顿迭代法的基础上,对开平方计算的牛顿迭代法进行了改进。改进方法综合了查表法以及牛顿迭代法,运算过程中只需要一次牛顿迭代计算,根据精度要求定量地确定表格大小。通过实例验证了该方法具有运算速度快、精度高、占用内存小的特点,解决了长期以来开平方算法存在耗时长、精度低、存贮数据值范围难以确定的问题。

Based on the analysis of the look-up table method and Newton iteration algorithm the paper improves the Newton iteration method for the square root calculation. The advanced method integrates the look-up table method and Newton iteration method. Only one cycle of Newton iteration is needed in the operation process and the size of the table can been quantificationally determined by the precision require. Examples show that the method has the properties of fast operation ,high precision and memory saving,which solves the problems of time waste, low precision and the scope of stored data value difficult to determine in the square root calculation over a long period.