| 矩阵方程AXA~T+BYB~T+AZB~T=D的(局部)对称最小二乘解 |
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| 引用本文： | 孙庆娟,郭文彬,江春林.矩阵方程AXA~T+BYB~T+AZB~T=D的(局部)对称最小二乘解[J].烟台大学学报(自然科学与工程版),2013,26(1):4-8. |
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| 作者姓名： | 孙庆娟 郭文彬 江春林 |
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| 作者单位： | 1. 聊城大学数学科学学院,山东聊城252059;潍坊市寒亭区第一中学,山东潍坊261100
2. 潍坊市寒亭区第一中学,山东潍坊,261100 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 矩阵方程问题在结构设计、系统识别、振动理论等领域有着广泛的应用.对于任意给定的矩阵A∈Rm×n,B∈Rm×n,D∈Rm×m,本文利用奇异值分解和Kronecker积给出了矩阵方程AXAT+BYBT+AZBT=D的局部对称最小二乘解,并在一定条件下得出了方程的对称最小二乘解.
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| 关 键 词： | 奇异值分解 Kronecker积 对称矩阵 最小二乘解 |
The Least Squares (Locally) Symmetric Solutions of the Matrix Equation AXAT + BYBT + AZBT =D |
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| SUN Qing-juan
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GUO Wen-bin
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JIANG Chun-lin.The Least Squares (Locally) Symmetric Solutions of the Matrix Equation AXAT + BYBT + AZBT =D[J].Journal of Yantai University(Natural Science and Engineering edirion),2013,26(1):4-8. |
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| Authors: | SUN Qing-juan GUO Wen-bin JIANG Chun-lin |
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| Institution: | 1. School of Mathematics Science, Liaocheng University, Liaoeheng 252059, China;2. Hanting NO. 1 Middle School in Weifang, We- ifang 261100, China) |
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| Abstract: | The matrix equation problem has been widely used in many fields such as structure design, system iden- tification, vibration theory and so on. For given matrices ,A RTM ,B ∈ R ,D ∈R , the least squares locally symmetric solutions of the matrix equation AXAT ＋ BYBT ＋AZBT =D are obtained by using the singular value de- composition and the Kroneeker product of matrices. Under certain conditions, we also give the least squares sym- metric solutions of the preceding matrix equation. |
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| Keywords: | singular value decomposition kronecker product symmetric matrix least squares solution |
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