A model order reduction scheme of the transient response of large-scale randomly parametrized linear finite element system in state space form has been proposed. The reduced order model realization is aimed at preserving the invariant properties of the dynamic system model based on the dominant coupling characteristics of the specified system inputs and outputs. An a-priori model reduction stra...

This paper presents a model order reduction method via Krylov subspace projection, for applications in the field of computational electromagnetics (CEM). The approach results to be suitable both for SISO and MIMO systems, and is based on the numerically robust Arnoldi procedure. We have studied the model order reduction as the number of inputs and outputs changes, to better understand the behav...

A bstract Inspired by the universal operator growth hypothesis, we extend formalism of Krylov construction in dissipative open quantum systems connected to a Markovian bath. Our is based upon modification Liouvillian superoperator appropriate Lindbladian, thereby following vectorized Lanczos algorithm and Arnoldi iteration. This well justified due incorporation non-Hermitian effects environment...

A multigrid-type method has been developed for nding quasi-stationary distributions of structured continuous-time Markov chains. Finding quasi-stationary distributions is equivalent to nding the eigenvector of the smallest eigenvalue of the deening matrix of the continuous-time Markov chain. The multigrid-type method used here is not equivalent to inverse iteration, and does not use the multigr...

The overlap Dirac operator at nonzero quark chemical potential involves the computation of the sign function of a non-Hermitian matrix. In this talk we present iterative Krylov subspace approximations, with deflation of critical eigenvalues, which we developed to compute the operator on large lattices. We compare the accuracy and efficiency of two alternative approximations based on the Arnoldi...

The restarted generalized minimum residual method (RGMRES) (Saad and Schultz (1986), Barrett et al. (1994), Dias da Cunha and Hopkins (1994)) starts from the residual r0 1⁄4 b Ax0, where x0 is an initial estimate for the solution (often x0 1⁄4 0). An orthogonal basis for the Krylov subspace spanfAr0g, for k 1⁄4 0; 1; 2; . . ., is generated explicitly: this is referred to as Arnoldi’s method (Ar...

We consider the nonlinear eigenvalue problem: M(λ)x = 0, where M(λ) is a large parameter-dependent matrix. In several applications, M(λ) has a structure where the higher-order terms of its Taylor expansion have a particular low-rank structure. We propose a new Arnoldi based algorithm that can exploit this structure. More precisely, the proposed algorithm is equivalent to Arnoldi’s method applie...

Generalized block Lanczos methods for large unsymmetric eigenproblems are presented, which contain the block Arnoldi method, and the block Arnoldi algorithms are developed. The convergence of this class of methods is analyzed when the matrix A is diagonalizable. Upper bounds for the distances between normalized eigenvectors and a block Krylov subspace are derived, and a priori theoretical error...