On Solving the Large Sparse Generalized Eigenvalue Problem

145 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1981.This thesis presents an algorithm for solving the large sparse generalized eigenvalue problem Ax = (lamda)Bx. The matrices A and B are assumed to be symmetric, and haphazardly sparse, with B being positive definite. The problem is treated from a constrained optimization approach and an inverse iteration is developed which requires the solution of linear algebraic systems only to the accuracy demanded by a given subspace. The convergence of the method is discussed, and the rate of convergence is improved by using shifting with the Ritz approximations. Numerical results are presented, and aspects concerning an implementation on a parallel computer are discussed.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD