Partial solution of eigenproblems by a decomposition method-1. Theory

This paper demonstrates the feasibility of using a recently developed technique, the ‘r-variable algorithm’ (see references under Ng), to solve the partial enginproblem. The method involves decomposing the Rayleigh quotient minimization problem into smaller subproblems, where each subproblem is comprised of the solution of a system of linear equations using backward and forward substitutions. The striking features of the method lie in its simplicity and the minimal storage requirements. Examples are included to illustrate the accuracy of the approach in solving symmetric eigenproblems.