The Minimal Norm Least Squares Solutions for a Class of Matrix Equations
DOI: 10.54647/mathematics11371 76 Downloads 4899 Views
Author(s)
Abstract
In this paper, the minimal norm least squares solution of matrix equations (AXC,BXD,AXD,BXC)=(E,F,G,H) is discussed, by using the projection theorem, the generalized singular value decomposition and the canonical correlation decomposition, the expression of the solution of this problem is obtained.
Keywords
Minium-norm least-square solution; the Generalized Singular Value Decomposition; the Canonical Correlation Decomposition; the Projection Theorem
Cite this paper
Jinrong Shen,
The Minimal Norm Least Squares Solutions for a Class of Matrix Equations
, SCIREA Journal of Mathematics.
Volume 7, Issue 6, December 2022 | PP. 132-138.
10.54647/mathematics11371
References
[ 1 ] | Chen X T. Common solutions of a class of matrix equations. Numerical Mathematics A Journal of Chinese. 2005, 27(2):133-148. |
[ 2 ] | X.Yuan. On the two class of best approximation problems. Math.Numerica Sinica. 2001, 23:429-436. |
[ 3 ] | H.Golub, C.F.Van Loan. Matrix Computations. The Johns Hopkins Univ Press, Baltimore, MD, 1997. |
[ 4 ] | G.W.Setward, J.G.Sun. Matrix Perturbation Theory. Academic Press, New York,1990. 1998, 279:93-109. |
[ 5 ] | R.S.Wang. Functional Analysis and Optimization Theory. Beijing University of Aeronautics & Astronautics Press ,Beijing, 2003. |
[ 6 ] | Golub G H, Vanloan C F. Matrix Computation. Baltimore: Johns Hopkins University Press, 1996, 53-644. |
[ 7 ] | Liao A P, Lei Y, Yuan S F. The matrix nearness problem for symmetric matrices associated with the matrix equation [ATXA,BTXB]=[C,D]. Linear Algebra and Its Applications, 2006, 418: 939-954. |
[ 8 ] | Zhang S B, Deng Y. Reflexive solutions and antireflexive solutions of matrix equation AXB+CYD=E. Journal of Northeast Normal University (Natural Science Edition). 2022, 54(02):1-4. |
[ 9 ] | Ma Y, Huang X F. The solution of inverse Hermite matrix equation. University Mathematics. 2022,38(04):121-124. |