Accelerated subspace iteration using adaptive multiple inverse iteration

Previous research by the authors indicated that acceleration of the subspace iteration method might be achieved by performing multiple inverse iterations on the trial vectors corresponding to higher eigenvalues. A criterion, based on an estimate of each eigenvalue's rate of convergence, was used to choose the trial vectors which would undergo this acceleration. A new criterion is proposed to overcome certain limitations of the previous method. The new criterion is more robust and in many cases more efficient than the previous criterion. In the numerical examples presented, savings of up to 66%, in the number of multiplication operations, are obtained. An overrelaxation procedure is also combined with the two selective multiple inverse iteration criteria and the results are discussed. (C) 1997 Elsevier Science Ltd.