Parallel implementations for solving generalized eigenvalue problems with symmetric sparse matrices (Q685967)

The authors consider the solution of the generalized eigenvalue problem \(Ax = \lambda Mx\), where \(A\) and \(M\) are real symmetric matrices and \(M\) is positive definite. They compare numerically three algorithms: Reduction to a standard eigenvalue problem, multisectioning with Sturm sequences, and the Lanczos method. In the first algorithm the use of one vector processor for an effective Givens transformation is discussed. Parallel implementations for the following two algorithms are considered. All the tests are performed on matrices which belong to the Harwell- Boeing set of test matrices.