DYKSTRAS ALGORITHM FOR CONSTRAINED LEAST-SQUARES RECTANGULAR MATRIX PROBLEMS

In a recent paper, the authors applied Dykstra's alternating projectio n algorithm to solve constrained least-squares n x n matrix problems. We extend these results in two different directions. First, we make us e of the singular value decomposition to solve now constrained least-s quares rectangular m x n matrix problems that arise in several applica tions. Second, we propose a new and improved implementation of the pro jection algorithm onto the epsilon-positive definite set of matrices. This implementation does not require the computation of all eigenvalue s and eigenvectors of a matrix per iteration, and still guarantees con vergence. Finally, encouraging preliminary numerical results are discu ssed.