Sylvester方程在矩阵扰动分析中的应用

§1.引言 矩阵扰动分析的研究对于矩阵论的发展及数值分析问题计算结果的分析和处理都有重要意义.有关特征值、广义特征值及最小二乘问题的主要研究结果均含于1]中,5]运用二次方程根的判别法通过对代数Ricatti方程的解的估计给出了QR分解因子及Cholesky因子的扰动分析,但论证方法及所得结果都比较复杂且所求条件很强.3]和

On the Application of Sylvester Equation to Matrix Perturbation Problems

This paper deals with matrix perturbation problems by means of Sylvester matrix equations.The new approach is simple in the demonstration and the perturbation bounds obtained are moreaccurate for some problems, such as QR factorization, Cholesky factors, eigenvalues of a matrixand deflating-pairs of regular matrix-pencils. A new and straightforward proof for the pertur-bation theorem on polar decomposition is also given.