Selective alternating projections to find the nearest SDD+ matrix

摘要

We extend and improve recently proposed algorithms to solve the problem of minimizing the distance from a given matrix to the cone of symmetric and diagonally dominant matrices with positive diagonal (SDD+). We present a variety of criteria to select a subset of the supporting hyperplanes of the faces of SDD+, and also of the polar cone (SDD+)0, to then apply Dykstra’s alternating projection method. These selections reduce the number of projections and therefore reduce the required computational work. In all our new algorithms, the symmetry and the diagonal dominance of the obtained matrix are guaranteed. Preliminary numerical experiments indicate that some of the selection criteria produce a significant reduction in CPU time.