Linear Algebra Seminar

Speaker: An-Bao Xu

Title: Least-squares symmetric solution to the matrix equation A X B = C with the norm inequality constraint

In this talk, we are going to discuss an iterative method to compute symmetric least-squares solution of the matrix equation A X B = C with the norm inequality constraint,

$$\begin{equation*} \mathop {\min }\limits_{X \in SR^{n\times n}} \textstyle{1 \over 2}\left\| {A\, X\, B\, - \,C} \right\|^2 \quad subject\ to \left\| X \right\| \le \Delta, \end{equation*}$$
where $A\in R^{p\times n}$, $B\in R^{n\times q}$, $C\in R^{p\times q}$, and $\Delta$ is a nonnegative real number.

For this method, without the error of calculation, a desired solution can be obtained with finitely iterate steps. Numerical experiments are performed to illustrate the efficiency and application of the algorithm.

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