Anderson(m0) extrapolation, an accelerator to a fixed-point iteration, stores m0+1 prior evaluations of the iteration and computes linear combination those as new iteration. The computational cost acceleration becomes expensive with parameter m0 increasing, thus is common choice in most practice. In this paper, aim improving computations PageRank problems, method was developed by applying Ander...

We propose a restarted Arnoldi’s method with Faber polynomials and discuss its use for computing the rightmost eigenvalues of large non hermitian matrices. We illustrate, with the help of some practical test problems, the benefit obtained from the Faber acceleration by comparing this method with the Chebyshev based acceleration. A comparison with the implicitly restarted Arnoldi method is also ...

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...

Since the rst papers on asymptotic waveform evaluation (AWE), Pad e-based reduced order models have become standard for improving coupled circuit-interconnect simulation eeciency. Such models can be accurately computed using bi-orthogonalization algorithms like Pad e via Lanczos (PVL), but the resulting Pad e approximates can still be unstable even when generated from stable RLC circuits. For c...

We present an efficient inexact implicitly restarted Arnoldi algorithm to find a few eigenpairs of large unitary matrices. The approximating Krylov spaces are built using short-term recurrences derived from Gragg’s isometric Arnoldi process. The implicit restarts are done by the KrylovSchur methodology of Stewart. All of the operations of the restart are done in terms of the Schur parameters ge...

In this paper, we propose a highly e cient accelerating method for the restarted Arnoldi iteration to compute the eigenvalues of a large nonsymmetric matrix. Its e ectiveness is proved by various numerical experiments and comparisons with other approaches. Several new results on the characteristics of the polynomial acceleration are also reported. The Arnoldi iteration has been the most popular...

We present an algorithm for determining the stability of delay differential equations (DDEs)with time-periodic coefficients and time-periodic delays. The DDEs are first posed as an equivalent system of partial differential equations (PDEs) along with a nonlinear boundary condition. A Galerkin approximation is then employed to discretize the PDEs into a set of time-periodic ordinary differential...