Author(s)

Chunmei Li^*, Xuefeng Duan, Zhuling Jiang

College of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin, China.

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 AXB = E, CXD = F. If we choose the initial iterative matrix X₀ = 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.

Matrix Equation, Dykstra’s Alternating Projection Algorithm, Optimal Approximate Solution, Least Norm Solution

Li, C. , Duan, X. and Jiang, Z. (2016) Dykstra’s Algorithm for the Optimal Approximate Symmetric Positive Semidefinite Solution of a Class of Matrix Equations. Advances in Linear Algebra & Matrix Theory, 6, 1-10. doi: 10.4236/alamt.2016.61001.