PRECONDITIONERS FOR DISTANCE MATRIX ALGORITHMS

A recent gradient algorithm in nonlinear optimization uses a novel ide a that avoids line searches. This so-called spectral gradient algorith m works well when the spectrum of the Hessian of the function to be mi nimized has a small range or is clustered. In this article, we find a general preconditioning method for this algorithm. The preconditioning method is applied to the stress function, which arises in many applic ations of distance geometry, from statistics to finding molecular conf ormations. The Hessian of stress is shown to have a nice block structu re. This structure yields a preconditioner which decreases the amount of computation needed to minimize stress by the spectral gradient algo rithm. (C) 1994 by John Wiley and Sons, Inc.