CONJUGATE-GRADIENT METHODS FOR THE RAYLEIGH QUOTIENT MINIMIZATION OF GENERALIZED EIGENVALUE PROBLEMS

Here we consider a modified version of the Rayleigh quotient conjugate gradient method of Bradbury and Fletcher for the computation of the smallest eigenvalue and a corresponding eigenvector of Ax = lambdaBx, where A and B are real symmetric and B is positive definite. Global convergence to an eigenpair is proved and, under certain conditions, convergence to the lowest eigenpair is obtained.