Dykstraʹs algorithm for constrained least-squares rectangular matrix problems

In a recent paper, the authors applied Dykstraʹs alternating projection algorithm to solve constrained least-squares n × n matrix problems. We extend these results in two different directions. First, we make use of the singular value decomposition to solve now constrained least-squares rectangular m × n matrix problems that arise in several applications. Second, we propose a new and improved implementation of the projection algorithm onto the -positive definite set of matrices. This implementation does not require the computation of all eigenvalues and eigenvectors of a matrix per iteration, and still guarantees convergence. Finally, encouraging preliminary numerical results are discussed.