For computing PageRank problems, a Power–Arnoldi algorithm is presented by periodically knitting the power method together with thick restarted Arnoldi algorithm. In this paper, using extrapolation process based on trace (PET), variant of developed for accelerating computations. The new called Arnoldi-PET algorithm, whose implementation and convergence are analyzed. Numerical experiments severa...

A generalized refined Arnoldi method based on the weighted inner product is presented for computing PageRank. The properties of the generalized refined Arnoldi method were studied. To speed up the convergence performance for computing PageRank, we propose to change the weights adaptively where the weights are calculated based on the current residual corresponding to the approximate PageRank vec...

In this paper we introduce a two-sided Arnoldi method that can be used in the reduction of high order systems, based on a two-sided Krylov subspace approach. The presented method can find better results than the well known Arnoldi algorithm and leads to the same reduced models as the (numerically unstable and more complicated) Lanczos algorithm. The new algorithm can find two orthogonal bases f...

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...

The implicitly restarted Arnoldi method implicitly applies a polynomial lter to the Arnoldi vectors by use of orthogonal transformations. In this paper, an implicit ltering by rational functions is proposed for the rational Krylov method. This ltering is performed in an eecient way. Two applications are considered. The rst one is the ltering of unwanted eigenvalues using exact shifts. This appr...

The Quadratic Arnoldi algorithm is an Arnoldi algorithm for the solution of the quadratic eigenvalue problem, that exploits the structure of the Krylov vectors. This allows us to reduce the memory requirements by about a half. The method is an alternative to the Second Order Arnoldi method (SOAR). In the SOAR method it is not clear how to perform an implicit restart. We discuss various choices ...

This paper proposes a block Arnoldi method for parameterized model order reduction. This method works when design parameters have only low-rank impacts on the system matrix. The method preserves all design parameters in the reduced model and is easy to implement. Numerical results show that the block Arnoldi process outperforms some existing methods up to a factor of ten.

Title of dissertation: Residual Arnoldi Methods : Theory, Package, and Experiments Che-Rung Lee, Doctor of Philosophy, 2007 Dissertation directed by: Professor G.W. Stewart Department of Computer Science This thesis is concerned with the solution of large-scale eigenvalue problems. Although there are good algorithms for solving small dense eigenvalue problems, the large-scale eigenproblem has m...

Global projection methods have been used for solving numerous large matrix equations, but nothing has been known on if and how a global projection method can be proposed for solving large eigenproblems. In this paper, based on the global Arnoldi process that generates an Forthonormal basis of a matrix Krylov subspace, a global Arnold method is proposed for large eigenproblems. It computes certa...

The explicitly restarted Arnoldi method (ERAM) allows one to find a few eigenpairs of a large sparse matrix. The multiple explicitly restarted Arnoldi method (MERAM) is a technique based upon a multiple projection of ERAM and accelerates its c S i t c a t ©