研究摄动离散矩阵Lyapunov方程解的向后误差,利用矩阵Kronecker积的性质以及矩阵范数的性质,给出方程近似解的向后误差界,最后通过数值例子说明解的向后稳定性.
The backward error of the solution to the perturbed discrete matrix Lyapunov equation is studied. The backward error bounds of the approximation positive definite solution to the equation are presented by using the property of matrix Kronecker products and matrix norms. Finally, the stability of above results is shown by a numerical example.