The two-phase method for finding a great number of eigenpairs of the symmetric or weakly non-symmetric large eigenvalue problems (Q1326718)

An iterative method to solve eigenproblems \(Ax = \lambda Bx\), where the matrices \(A\) and \(B\) are symmetric, large \((N \sim 100000)\) and sparse and where \(B\) is positive definite, is presented, analyzed and compared with some traditional numerical procedures. The method is a combination of two methods: the subspace iteration and the Rayleigh quotient iteration. Its extension to weakly non-symmetric problems is given.