Efficient Solution of Large-Scale Electromagnetic Eigenvalue Problems using the Implicitly Restarted Arnoldi Method

Implicitly Restarted Arnoldi/lanczos Methods for Large Scale Eigenvalue Calculations

This report provides an introductory overview of the numerical solution of large scale algebraic eigenvalue problems. The main focus is on a class of methods called Krylov subspace projection methods. The Lanczos method is the premier member of this class and the Arnoldi method is a generalization to the nonsymmetric case. A recently developed and very promising variant of the Arnoldi/Lanczos s...

ARPACK users' guide - solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods

Some new restart vectors for explicitly restarted Arnoldi method

The explicitly restarted Arnoldi method (ERAM) can be used to find some eigenvalues of large and sparse matrices. However, it has been shown that even this method may fail to converge. In this paper, we present two new methods to accelerate the convergence of ERAM algorithm. In these methods, we apply two strategies for the updated initial vector in each restart cycles. The implementation of th...

Partial Eigenvalue Assignment for Large Observer Problems

The construction of a closed-loop observer for linear control systems and the associated eigenvalue assignment problem are classical tasks in Control Theory. The present paper describes an algorithm for the solution of this eigenvalue assignment problem. The algorithm is based on the implicitly restarted Arnoldi method, and is well suited for large-scale problems, that require the (re)assignmen...

Implicitly Restarted Arnoldi Methods and Eigenvalues of the Discretized Navier Stokes Equations

Implicitly restarted Arnoldi methods and eigenvalues of the discretized Navier Stokes equations. Abstract We are concerned with nding a few eigenvalues of the large sparse nonsymmetric generalized eigenvalue problem Ax = Bx that arises in stability studies of incompressible uid ow. The matrices have a block structure that is typical of mixed nite-element discretizations for such problems. We ex...