Dykstra's algorithm for constrained least-squares doubly symmetric matrix problems

Authors:
Jiao-fen Li;Xi-yan Hu;Lei Zhang
Affiliations:
School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, PR China;College of Mathematics and Econometrics, Hunan University, Changsha 410082, PR China;College of Mathematics and Econometrics, Hunan University, Changsha 410082, PR China
Venue:
Theoretical Computer Science
Year:
2010

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Abstract

In this work we apply Dykstra's alternating projection algorithm for minimizing @?AX-B@? where @?@?@? is the Frobenius norm and A@?R^m^x^n, B@?R^m^x^n and X@?R^n^x^n are doubly symmetric positive definite matrices with entries within prescribed intervals. We first solve the constrained least-squares matrix problem by using the special structure properties of doubly symmetric matrices, and then use the singular value decomposition to transform the original problem into a simpler one that fits nicely with the algorithm originally developed by [R. Escalante, M. Raydan, Dykstra's algorithm for a constrained least-squares matrix problem, Numer. Linear Algebra Appl. 3 (1996) 459-471].