Fast enclosure of matrix eigenvalues and singular values via rounding mode controlled computation
Fast enclosure of matrix eigenvalues and singular values via rounding mode controlled computation
复制标题
通过舍入模式控制计算快速封装矩阵特征值和奇异值
DOI：
10.1016/s0024-3795(00)00272-x
复制
发表时间：
2001
影响因子：
1.1
通讯作者：
S. Oishi
中科院分区：
文献类型：
--
作者：
S. Oishi
对矩阵特征值和奇异值问题的Bauer-Fike型和Weyl型摄动定理进行了修正。结果表明，所提出的定理的条件可以严格检查的浮点计算舍入模式控制。强调了在matlab等常用数值计算软件上可以方便地构造验证程序。对于一个真实的对称n×n矩阵，得到严格的特征值误差界的计算代价为6 n3次浮点运算.
Modifications of Bauer–Fike type and Weyl type perturbation theorems are presented for matrix eigenvalue and singular value problems. It is shown that the conditions of the presented theorems can be rigorously checked by floating point computation with rounding mode control. It is stressed that verification programs can be easily constructed on usual numerical softwares like matlab. Computational cost of obtaining rigorous error bounds for computed eigenvalues is shown to be 6n3flops for a real symmetric n×n matrix.