一种实对称矩阵特征值的求法

A Arithmetic of Real Symmetry Matrix Eigenvalues

运用正交相似变换将实对称矩阵约化为不可约对称三对角矩阵,依不可约对称三对角矩阵特征值的隔离性质,构造出具有分段严格单调性的等价模型,证明在每一单调区间内有且仅有一个根,并采用具有二次收敛的Newton迭代法求解.最后,给出了算法及算例.

We can transform the real symmetry matrix into unreduced symmetric tridiagonal matrix with Similitude transform. According to isolation property an unreduced symmetric tridiagonal matrix with eigenvalues, we can give an equivalence model with subsection strict monotonically. The paper points out it has only a root in each monotony section. So we can solve it with Newton iterative arithmetic of square convergent. Finally, arithmetic and an example are given.