An Alternating Projection Algorithm for Computing the Nearest Euclidean Distance Matrix
W. Glunt, T. L. Hayden, S. Hong, J. H. Wells · SIAM Journal on Matrix Analysis and Applications · 1990
Recent extensions of von Neumann’s alternating projection algorithm permit an effective numerical approach to certain least squares problems subject to side conditions. This paper treats the problem of minimizing the distance from a given symmetric matrix to the class of Euclidean distance matrices; in dimension $n = 3$ we obtain the solution in closed form.