论文标题
一类准线性矩阵方程的数值解
Numerical solution of a class of quasi-linear matrix equations
论文作者
论文摘要
Given the matrix equation ${\bf A X} + {\bf X B} + f({\bf X }) {\bf C} ={\bf D}$ in the unknown $n\times m$ matrix ${\bf X }$, we analyze existence and uniqueness conditions, together with computational solution strategies for $f \,: \ Mathbb {r}^{n \ times m} \ to \ mathbb {r} $是线性或非线性函数。我们表征矩阵方程式及其解决方案的不同属性，具体取决于所考虑的函数类别$ f $。我们的分析主要涉及小小的问题，尽管几个考虑因素也适用于大型矩阵方程。
Given the matrix equation ${\bf A X} + {\bf X B} + f({\bf X }) {\bf C} ={\bf D}$ in the unknown $n\times m$ matrix ${\bf X }$, we analyze existence and uniqueness conditions, together with computational solution strategies for $f \,: \mathbb{R}^{n \times m} \to \mathbb{R}$ being a linear or nonlinear function. We characterize different properties of the matrix equation and of its solution, depending on the considered classes of functions $f$. Our analysis mainly concerns small dimensional problems, though several considerations also apply to large scale matrix equations.
