求解二阶Sylvester矩阵方程EXF2+AXF+CX+BY=D的矩阵形式LSQR迭代法

2010 International Conference on Computational Intelligence and Software Engineering Pub Date : 2010-12-30 DOI:10.1109/CISE.2010.5676729

Sheng-Kun Li

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引用次数: 0

摘要

本文基于LSQR算法的矩阵形式，提出了一种求解未知矩阵对[X, Y]的二阶Sylvester矩阵方程EXF^{2}+AXF+CX+BY=D的迭代方法。通过这种迭代方法，我们可以得到对称矩阵、广义双对称矩阵和(R, S)对称矩阵上的最小Frobenius范数解对或最小Frobenius范数最小二乘解对。

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A Matrix-Form LSQR Iterative Method for Solving the Second-Order Sylvester Matrix Equation EXF2+AXF+CX+BY=D

In this paper, an iterative method is proposed to solve the second-order Sylvester matrix equation EXF^{2}+AXF+CX+BY=D with unknown matrix pair [X, Y], based on a matrix form of LSQR algorithm. By this iterative method, we can obtain the minimum Frobenius norm solution pair or the minimum Frobenius norm least squares solution pair over some constrained matrices, such as symmetric, generalized bisymmetric and (R, S)-symmetric matrices.

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2010 International Conference on Computational Intelligence and Software Engineering

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