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李水勤, 邓继恩, 杨娟. 矩阵方程A~TXA=B的双反对称最小二乘解及其最佳逼近[J]. 信阳师范学院学报(自然科学版), 2011, 24(2): 183-187.
引用本文: 李水勤, 邓继恩, 杨娟. 矩阵方程A~TXA=B的双反对称最小二乘解及其最佳逼近[J]. 信阳师范学院学报(自然科学版), 2011, 24(2): 183-187.
shu
LI Shui-qin, DENG Ji-en, YANG Juan. Least-squares Solutions of Anti-bisymmetric Matrices to Matrix Equation A~TXA=B and Their Optimal Ap[J]. Journal of Xinyang Normal University (Natural Science Edition), 2011, 24(2): 183-187.
Citation: LI Shui-qin, DENG Ji-en, YANG Juan. Least-squares Solutions of Anti-bisymmetric Matrices to Matrix Equation A~TXA=B and Their Optimal Ap[J]. Journal of Xinyang Normal University (Natural Science Edition), 2011, 24(2): 183-187.
shu

矩阵方程A~TXA=B的双反对称最小二乘解及其最佳逼近

Least-squares Solutions of Anti-bisymmetric Matrices to Matrix Equation A~TXA=B and Their Optimal Ap

    摘要
  • 摘要: 利用矩阵对的标准相关分解、广义奇异值分解和投影定理,给出了矩阵方程ATXA=B的双反对称最小二乘解的一般表达式,在此基础上,求出了给定矩阵的最佳逼近.

     

    Abstract: According to the canonical correlation decomposition of a pair of matrices,generalized singular value decomposition and the projection theorem,the expression of the least-squares solutions of anti-bisymmetric matrices to matrix equation ATXA=B is given.Based on this result,the optimal approximate solution to a given matrix is also derived

     

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