Simultaneous Iteration for Partial Eigensolution of Real Matrices

Simultaneous iteration methods are presented for obtaining dominanteigenvalues and corresponding eigenvectors of real unsymmetricmatrices. These methods involve the accurate eigensolution ofthe smaller interaction matrix at each iteration, the dimensionsof which depend on the number of vectors processed simultaneously.A bi-iteration procedure is proposed when both left and righteigenvectors are required, and a lopsided iteration procedurewhen only one set of eigenvectors is required. Numerical testsare discussed.