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| 摘要: |
| 本文研究了半张量积下矩阵方程组AX=B，XC=D在不同情况下的最小二乘解X*∈Rp×q，其中矩阵A∈Rm×n，B∈Rh×k，C∈Ra×b，D∈Rl×d给定.根据半张量积的定义将其转变为普通乘积下的矩阵方程组，再结合矩阵奇异值分解及矩阵微分给出该方程组在不同情况下最小二乘解的解析表达式，并用数值算例加以验证. |
| 关键词: 半张量积 矩阵方程组 最小二乘解 奇异值分解 |
| DOI： |
| 分类号:O214.6 |
| 基金项目:国家自然科学基金资助（11301107；11561015）；广西自然科学基金资助（2016GXNSFAA380074；2016GXNSFFA380009）. |
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| LEAST-SQUARES SOLUTIONS OF MATRIX EQUATIONS AX=B,XC=D WITH SEMI-TENSOR PRODUCT |
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LI Tao,ZHOU Xue-lin,LI Jiao-fen
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| Abstract: |
| In this paper, we consider the least-square solutions X*∈Rp×q of the matrix equations AX=B,XC=D with respect to the semi-tensor product, where matrices A∈Rm×n,B∈Rh×k,C∈Ra×b,D∈Rl×d are given. By using the definition of the semi-tensor product, we transform the original problem under semi-tensor product into some related matrix least squares with the conventional matrix product. Then, combining with the differentiation and singular value decomposition of matrices, we give the explicit representation of the least squares solution. Finally, we present some elementary numerical examples to verify the proposed results. |
| Key words: semi-tensor product matrix equations least-squares solution singular value decomposition |
