The m-order Jacobi, Gauss–Seidel and symmetric Gauss–Seidel methods

Two modified Jacobi methods for M-matrices

Jacobi-Davidson Methods for Symmetric Eigenproblems

1 Why and how The Lanczos method is quite eeective if the desired eigenvalue is either max or min and if this eigenvalue is relatively well separated from the remaining spectrum, or when the method is applied with (A ? I) ?1 , for some reasonable guess for an eigenvalue. If none of these conditions is fulllled, for instance the computation of a vector (A ? I) ?1 y for given y may be computation...

two modified jacobi methods for m-matrices

Restarting Techniques for the (jacobi-)davidson Symmetric Eigenvalue Methods

The (Jacobi-)Davidson method, which is a popular preconditioned extension to the Arnoldi method for solving large eigenvalue problems, is often used with restarting. This has significant performance shortcomings, since important components of the invariant subspace may be discarded. One way of saving more information at restart is through “thick” restarting, a technique that involves keeping mo...

Multigrid Methods for Second Order Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Bellman-Isaacs Equations

We propose multigrid methods for solving the discrete algebraic equations arising from the discretization of the second order Hamilton–Jacobi–Bellman (HJB) and Hamilton– Jacobi–Bellman–Isaacs (HJBI) equations. We propose a damped-relaxation method as a smoother for multigrid. In contrast with the standard policy iteration, the proposed damped-relaxation scheme is convergent for both HJB and HJB...