Computing the nearest diagonally dominant matrix

We solve the problem of minimizing the distance from a given matrix to the set of symmetric and diagonally dominant matrices. First, we characterize t he projection onto the cone of diagonally dominant matrices with positive d iagonal, and then we apply Dykstra's alternating projection algorithm on th is cone and on the subspace of symmetric matrices to obtain the solution. W e discuss implementation details and present encouraging preliminary numeri cal results. (C) 1998 John Wiley & Sons, Ltd.