【摘要】 对于被开方数为两数平方和形式的开方运算,为了简化运算并提高计算精度,提出了一种迭代开方算法。该算法选取一次多项式作为初值,利用泰勒级数展开得到简化算法。分析了简化算法的最大误差,确定了使得误差最小的一次多项式系数。在此基础上,给出了实用化的一次多项式系数和迭代计算公式。该迭代算法与牛顿迭代法在本质上是相同的,但无需考虑初值选取问题,因而计算精度仅取决于迭代次数。仿真证明,两次迭代的计算量与传统简化算法相当,但精度能提高100倍以上,误差不大于0.002%,可满足微机保护的计算精度要求。更多还原

【Abstract】 A new iterative square root algorithm is proposed to improve the precision of square root which is the sum of two squares.Taylor series is introduced to derive the formula by using the first polynomial as the initial value.The optimal coefficient of the first polynomial with minimal error is obtained based on the analysis of maximal error when the coefficient is distributed in different scope.Further,the practical coefficient of the first polynomial and iterative algorithm of square root is proposed,which is essentially same as Newton iteration method,but does not need to consider the initial value selection,and the precision depends on iteration times.The simulation shows that the computation complexity of the proposed algorithm is similar to the traditional method,but the precision is increased by 100 times.The maximal error is below the 0.002% and it meets the requirement of microprocessor protection.更多还原