Title :
The optimal approximation solution associated with a nonnegative definite constraint matrix equation
Author :
Xie, Cong-Xiu ; Zeng, Juan
Author_Institution :
Sch. of Sci., Beijing Inf. Sci. & Technol. Univ., Beijing, China
Abstract :
It is studied to find a positive semidefinite(not necessarily symmetric) matrix A satisying equation AX = B for given X, B. The solvable conditions are given and a general expression of the solutions is provided. The problem to find the positive semidefinite matrix  which minimizes A*-A in Frobenius norm is considered, where matrix A satisfies AX = B. Some numerical results are also reported.
Keywords :
matrix algebra; Frobenius norm; nonnegative definite constraint matrix equation; optimal approximation solution; positive semidefinite matrix; Cybernetics; Eigenvalues and eigenfunctions; Equations; Machine learning; Matrix decomposition; Symmetric matrices; Matrix equation; Positive semidefinite matrix; Singular value decomposition;
Conference_Titel :
Machine Learning and Cybernetics (ICMLC), 2010 International Conference on
Conference_Location :
Qingdao
Print_ISBN :
978-1-4244-6526-2
DOI :
10.1109/ICMLC.2010.5581083
