%0 Journal Article
%T Dykstra¡¯s Algorithm for the Optimal Approximate Symmetric Positive Semidefinite Solution of a Class of Matrix Equations
%A Chunmei Li
%A Xuefeng Duan
%A Zhuling Jiang
%J Advances in Linear Algebra & Matrix Theory
%P 1-10
%@ 2165-3348
%D 2016
%I Scientific Research Publishing
%R 10.4236/alamt.2016.61001
%X Dykstra¡¯s
alternating projection algorithm was proposed to treat the problem of finding
the projection of a given point onto the intersection of some closed convex
sets. In this paper, we first apply Dykstra¡¯s alternating projection algorithm
to compute the optimal approximate symmetric positive semidefinite solution of
the matrix equations <i>AXB</i> = <i>E</i>, <i>CXD</i> = <i>F</i>. If we choose the initial
iterative matrix <i>X</i><sub>0</sub> = 0,
the least Frobenius norm symmetric positive semidefinite solution of these
matrix equations is obtained. A numerical example shows that the new algorithm
is feasible and effective.
%K Matrix Equation
%K Dykstra¡¯s Alternating Projection Algorithm
%K Optimal Approximate Solution
%K Least Norm Solution
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=64247