We consider the class of the Orthogonal Projection Methods (OPM) to solve iteratively large and generalised eigenvalue problems. An OPM is a method that projects a large eigenvalue problem on a smaller subspace. In this subspace, an approximation of the eigenvalue spectrum can be computed from a small eigenvalue problem using a direct method. We show that many iterative eigenvalue solvers, such...

Restarted GMRES is known to be inefficient for solving shifted systems when the shifts are handled simultaneously. Variants have been proposed to enhance its performance. We show that another restarted method, restarted Full Orthogonalization Method (FOM), can effectively be employed. The total number of iterations of restarted FOM applied to all shifted systems simultaneously is the same as th...

We show how the Arnoldi algorithm for approximating a function of a matrix times a vector can be restarted in a manner analogous to restarted Krylov subspace methods for solving linear systems of equations. The resulting restarted algorithm reduces to other known algorithms for the reciprocal and the exponential functions. We further show that the restarted algorithm inherits the superlinear co...

It is known that the restarted full orthogonalization method (FOM) outperforms the restarted generalized minimum residual method (GMRES) in several circumstances for solving shifted linear systems when the shifts are handled simultaneously. On the basis of theWeightedArnoldi process, aweighted version of the Restarted Shifted FOM is proposed, which can provide accelerating convergence rate with...

Recently, structural symmetry breaking (SSB), a new technique for breaking all piecewise variable and value symmetry in constraint satisfaction problems (CSPs), was introduced. As of today, it is unclear whether the heavy symmetry filtering that SSB performs is at all worthwhile. This paper has two aims: First, we assess the feasibility of SSB. To this end, we introduce the first random benchma...

We present an approach for the acceleration of the restarted Arnoldi iteration for the computation of a number of eigenvalues of the standard eigenproblem Ax = x. This study applies the Chebyshev polynomial to the restarted Arnoldi iteration and proves that it computes necessary eigenvalues with far less complexity than the QR method. We also discuss the dependence of the convergence rate of th...