‎A matrix LSQR algorithm for solving constrained linear operator equations‎

In this work‎, ‎an iterative method based on a matrix form of LSQR algorithm is constructed for solving the linear operator equation $\mathcal{A}(X)=B$‎ ‎and the minimum Frobenius norm residual problem $||\mathcal{A}(X)-B||_F$‎ ‎where $X\in \mathcal{S}:=\{X\in \textsf{R}^{n\times n}~|~X=\mathcal{G}(X)\}$‎, ‎$\mathcal{F}$ is the linear operator from $\textsf{R}^{n\times n}$ onto $\textsf{R}^{r\times s}$‎, ‎$\mathcal{G}$ is a linear self-conjugate involution operator and‎ ‎$B\in \textsf{R}^{r\times s}$‎. ‎Numerical examples are given to verify the efficiency of the constructed method‎. ‎