In this paper, an iterative algorithm is presented to solve the Sylvester and Lyapunov matrix equations. By this iterative algorithm, for any initial matrix X1, a solution X＊ can be obtained within finite iteration s...In this paper, an iterative algorithm is presented to solve the Sylvester and Lyapunov matrix equations. By this iterative algorithm, for any initial matrix X1, a solution X＊ can be obtained within finite iteration steps in the absence of roundoff errors. Some examples illustrate that this algorithm is very efficient and better than that of [ 1 ] and [2].展开更多
Given a stable matrix A∈C<sup>n×n</sup>,there are some simple simultaneous inequalities whosecoefficients rely on A.For （?）P<sup>H</sup>=P∈C<sup>n×n</sup>,if P satisfi...Given a stable matrix A∈C<sup>n×n</sup>,there are some simple simultaneous inequalities whosecoefficients rely on A.For （?）P<sup>H</sup>=P∈C<sup>n×n</sup>,if P satisfies these inequlities,then PA+A<sup>H</sup>P【0.As anapplication of the main results,the stability of the matrix family is treated.Besides,some geometricproperties of the set of all the Lyapunov matrices of a given stable matrix are considered.展开更多
本文提出了一种新的求解李雅普诺夫方程的数值解法——U-D分解法.其基本思想是将解矩阵P分解为单位上三角阵U和非负定对角阵D,因此将 P 的迭代求解化为其因子 U 和 D 的迭代.这样,在计算量基本不变的情况下,提高了解的精度.本文还对[1]...本文提出了一种新的求解李雅普诺夫方程的数值解法——U-D分解法.其基本思想是将解矩阵P分解为单位上三角阵U和非负定对角阵D,因此将 P 的迭代求解化为其因子 U 和 D 的迭代.这样,在计算量基本不变的情况下,提高了解的精度.本文还对[1]中的加速收敛二步迭代法应用了 U-D 分解,使得该算法具有收敛快和精度高的双重优点.展开更多
基金supported by the National Natural Science Foundation of China (No.10771073)
文摘In this paper, an iterative algorithm is presented to solve the Sylvester and Lyapunov matrix equations. By this iterative algorithm, for any initial matrix X1, a solution X＊ can be obtained within finite iteration steps in the absence of roundoff errors. Some examples illustrate that this algorithm is very efficient and better than that of [ 1 ] and [2].
基金This work is supported by the National Natural Science Foundation of China
文摘Given a stable matrix A∈C<sup>n×n</sup>,there are some simple simultaneous inequalities whosecoefficients rely on A.For （?）P<sup>H</sup>=P∈C<sup>n×n</sup>,if P satisfies these inequlities,then PA+A<sup>H</sup>P【0.As anapplication of the main results,the stability of the matrix family is treated.Besides,some geometricproperties of the set of all the Lyapunov matrices of a given stable matrix are considered.
文摘本文提出了一种新的求解李雅普诺夫方程的数值解法——U-D分解法.其基本思想是将解矩阵P分解为单位上三角阵U和非负定对角阵D,因此将 P 的迭代求解化为其因子 U 和 D 的迭代.这样,在计算量基本不变的情况下,提高了解的精度.本文还对[1]中的加速收敛二步迭代法应用了 U-D 分解,使得该算法具有收敛快和精度高的双重优点.
