# ‎A matrix LSQR algorithm for solving constrained linear operator equations

Document Type: Research Paper

Author

Department of Mathematics Faculty of Mathematical Sciences Shahid Beheshti University, G.C., Evin, Tehran 19839 Iran

Abstract

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 $Xin mathcal{S}:={Xin textsf{R}^{ntimes n}~|~X=mathcal{G}(X)}$‎, ‎$mathcal{F}$ is the linear operator from $textsf{R}^{ntimes n}$ onto $textsf{R}^{rtimes s}$‎,
‎$mathcal{G}$ is a linear self-conjugate involution operator and‎
‎$Bin textsf{R}^{rtimes s}$‎.
‎Numerical examples are given to verify the efficiency of the constructed method‎.

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Main Subjects

### History

• Receive Date: 09 July 2012
• Revise Date: 05 December 2012
• Accept Date: 06 December 2012