一般地说,若一个非负数x的平方等于a,即x²=a,则这个数x叫做a的算术平方根。
当特征根难以求出而特征根的对称式易求时,半正定矩阵的算术平方根可直接由矩阵的本身的性质来表示。
On the other hand, square roots of semi-positive matrices can be expressed by the symmetric expression of eigenvalues, if the eigenvalues of semi-matrices are difficult to compute.
本文给出了在预定精确度下用迭代法计算算术平方根的方法,并分析了迭代的误差,给出了预定精确度下初始值的一个选取范围。
This paper gives a method to calculate the arithmetic square root by iteration with given accuracy, analyses the iteration error and provides a selected range of initial value with the given accuracy.
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