An orthogonal accelerated deflation technique for large symmetric eigenproblems

An improvement in accelerated conjugate gradient iterations is presented for the evaluation of several of the leftmost eigenpairs of large sparse symmetric positive definite matrices. The approach relies on an orthogonal deflation procedure and is based on the subsequent preconditioned conjugate gradient optimization of Rayleigh quotients over the restricted space orthogonal to the set of eigenvectors previously computed. Comparison with the accelerated simultaneous iterations performed over large finite element problems (with size up to 4500) shows that storage requirement is significantly less and CPU times may be reduced by a factor of two or more. © 1992.