Solving symmetric eigenvalue problem via genetic algorithms: Serial versus parallel implementation

We propose a new method for computing more than one eigenvalue of small and medium sized real symmetric matrices simultaneously by minimizing a suitably defined average Rayleigh Quotient (ρavρav) for the targeted group of eigenvalues by Genetic Algorithm. The proposed method is tested on two benchmark matrices of varying dimensions. Performance statistics is presented both as functions of dimensions of the matrices and as functions of the number of eigenvalues being sought simultaneously. A comparison is made with sequential search for multiple eigenvalues by minimization of Rayleigh Quotient with successive projections of unwanted eigenvectors. Parallel implementation of the algorithm shows an edge over its serial counterpart when larger number of eigenvalues are sought simultaneously and the dimensions of the matrices are higher.