‎a matrix lsqr algorithm for solving constrained linear operator equations

‎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 $Xin mathcal{S}:={Xin textsf{R}^{ntimes n}~|~X=mathcal{G}(X)}$‎, ‎$mathcal{F}$ is the linear operator from $textsf{R}^{ntimes n}$ onto $textsf{R}^{rtimes s}$‎, ‎$ma...

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 A(X) = B and the minimum Frobenius norm residual problem ||A(X)−B||F where X ∈ S := {X ∈ Rn×n | X = G(X)}, F is the linear operator from Rn×n onto Rr×s, G is a linear selfconjugate involution operator and B ∈ Rr×s. Numerical examples are given to verify the efficien...

A numerical algorithm for solving a class of matrix equations

In this paper, we present a numerical algorithm for solving matrix equations $(A otimes B)X = F$  by extending the well-known Gaussian elimination for $Ax = b$. The proposed algorithm has a high computational efficiency. Two numerical examples are provided to show the effectiveness of the proposed algorithm.

a numerical algorithm for solving a class of matrix equations

in this paper, we present a numerical algorithm for solving matrix equations $(a otimes b)x = f$  by extending the well-known gaussian elimination for $ax = b$. the proposed algorithm has a high computational efficiency. two numerical examples are provided to show the effectiveness of the proposed algorithm.

On the convergence of the Bl-LSQR algorithm for solving matrix equations

A new approach for solving the first-order linear matrix differential equations

Abstract. The main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. Properties of the Legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. Afterwards, an iterative algorithm is examined for solvin...