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Boyle, J.P. and Dykstra, R.L. (1986) A Method for Finding Projections onto the Intersections of Convex Sets in Hilbert Spaces. Lecture Notes in Statistics, 37, 28-47.

has been cited by the following article:

• TITLE: Dykstra’s Algorithm for the Optimal Approximate Symmetric Positive Semidefinite Solution of a Class of Matrix Equations

  AUTHORS: Chunmei Li, Xuefeng Duan, Zhuling Jiang

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

  JOURNAL NAME: Advances in Linear Algebra & Matrix Theory, Vol.6 No.1, March 7, 2016

  ABSTRACT: 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.