Stable calculation of coordinates from distance information

A new method is described for the calculation of Cartesian coordinates for n points given the n × n matrix of interpoint distances. The algorithm is faster than some earlier methods, and it is remarkably stable with respect to both numerical roundoff errors and errors in the given distance matrix. The resultant coordinates have their origin near the center of mass and axes approximately along the three principal rotational axes. The calculation is described of distances to the center of mass directly from the distance matrix. Results of computer trials of the algorithm are given.