数学与系统科学研究院

计算数学所学术报告

报告人：        Deng Yuanbei

Institute of Computational Mathematics and Scientific/Engineering Computing , CAS

报告题目 The Solutions of Several Classes　of Linear Matrix Equations and the Procrustes Problems

Abstract: The unconstrained and constrained linear matrix equations and related least squares(or Procrustes) problems have been of interest for many applications.
    By using of a series of methods in numerical linear algebra, such as the singular value decomposition (SVD) and the polar decomposition(PD) of a matrix, the generalized singular value decomposition (GSVD), the quotient singular value decomposition (QSVD) and the canonical correlation decomposition (CCD) of a pair of matrices, the generalized inverse of a matrix, the vector operator and the Kronecker product, the dual space theory and approximation principle in Hilbert space, the linear manifold and so on, a lot of constrained linear matrix equations, such as AX=B, AXB=C, AX+YA=C , AXA’+BYB’=C and the related least squares problems have been solved on the following problems.
1. The necessary and sufficient conditions for the existence of the matrix equations.
2.The gerenal expressions for the solutions of the matrix equations and the related least-squares problems .
3. The minimal norm solutions of some matrix equations and the related least-squares problems.
4. When the solution is unique, the logarithm is given.

报告时间：2003年12月10日  下午2：30-3：30

报告地点：科技综合楼三层报告厅