In recent years, high quality software for computing selected eigenvalues of large sparse nonsymmetric matrices has started to become publicly available. In this study we consider software which implements algorithms based on the original method of Arnoldi. We briefly describe the software which is available. We look at the key features of the codes and the important differences between them. T...

The eigenvalue assignment problem is a classical problem in Control Theory. This paper presents new algorithms for the stabilization of large single-input time-invariant control systems by partial eigenvalue assignment. Our algorithms are based on the implicitly restarted Arnoldi method, and are well suited for control systems that require the reassignment of a few eigenvalues.

In this paper we introduce a low cost method for integrating large dimensional linear initial value problems based on the Arnoldi algorithm for matrix functions. We also describe a very efficient step-size control technique and compare a resulting algorithm of order 4 with the standard Matlab solvers on linear stiff problems arising from the discretization of parabolic equations.

A reduced order multiport modeling algorithm based on the decomposition of the system transfer matrix into orthogonal scaled Laguerre functions is proposed. The link with Padé approximation, the block Arnoldi method and singular value decomposition leads to a simple and stable implementation of the algorithm.

In this note, we extend the Vandermonde with Arnoldi method recently advocated by Brubeck et al. (2021) to dealing confluent matrix. To apply process, it is critical find a Krylov subspace which generates column space of A theorem established for such subspaces any order derivatives. This enables us compute derivatives high degree polynomials precision. It also makes many applications involving...

Methods are presented for t ime evolution, steady-state solving and linear stability analysis for the incompressible Navier-Stokes equations at low to moderate Reynolds numbers. The methods use Krylov subspaces constructed by the Arnoldi process from actions of the explicit Navier-Stokes right-hand side and of its Jacobian, wi thout inversion of the viscous operator. Time evolut ion is performe...

This paper discusses the solution of large-scale linear discrete ill-posed problems with a noise-contaminated right-hand side. Tikhonov regularization is used to reduce the influence of the noise on the computed approximate solution. We consider problems in which the coefficient matrix is the sum of Kronecker products of matrices and present a generalized global Arnoldi method, that respects th...

Though the implicitly restarted Arnoldi/Lanczos method in ARPACK is a reliable method for computing a few eigenvalues of large-scale matrices, it can be inefficient because it only checks for convergence at restarts. Significant savings in runtime can be obtained by checking convergence at each Lanczos iteration. We describe a new convergence test for the maximum eigenvalue that is numerically ...

In this paper we investigate some practical aspects concerning the use of the Restricted-Denominator (RD) rational Arnoldi method for the computation of the core functions of exponential integrators for parabolic problems. We derive some useful a-posteriori bounds together with some hints for a suitable implementation inside the integrators. Numerical experiments arising from the discretization...