An Evaluation of Arnoldi based Software for Sparse Nonsymmetric Eigenproblems
نویسنده
چکیده
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. Then, using a wide range of practical problems, we compare the performance of the codes in terms of storage requirements, execution times, accuracy, and reliability, and consider their suitability for solving large-scale industrial problems. Finally, we point to possible future directions of research for improving Arnoldi based software. * Current reports available by anonymous ftp from seamus. cc . rl . ac .uk (internet 130.246.8.32) in the directory pub/reports. Argonne National Laboratory, Mathematics and Computer Science Division, Argonne, IL 60439, U.S.A. 2Computing and Information Systems Department, Atlas Centre, Rutherford Appleton Laboratory, Didcot, Oxfordshire OX1 1 OQX, England. March 18, 1996.
منابع مشابه
Weighted Harmonic Arnoldi Method for Large Interior Eigenproblems
The harmonic Arnoldi method can be used to find interior eigenpairs of large matrices. However, it has been shown that this method may converge erratically and even may fail to do so. In this paper, we present a new method for computing interior eigenpairs of large nonsymmetric matrices, which is called weighted harmonic Arnoldi method. The implementation of the method has been tested by numeri...
متن کاملLeast Squares Arnoldi for Large Nonsymmetric Eigenproblems
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...
متن کاملProjection Methods for Nonlinear Sparse Eigenvalue Problems
This paper surveys numerical methods for general sparse nonlinear eigenvalue problems with special emphasis on iterative projection methods like Jacobi–Davidson, Arnoldi or rational Krylov methods and the automated multi–level substructuring. We do not review the rich literature on polynomial eigenproblems which take advantage of a linearization of the problem.
متن کاملA Global Arnoldi Method for Large non-Hermitian Eigenproblems with Special Applications to Multiple Eigenproblems∗
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...
متن کاملAugmented Block Householder Arnoldi Method
Computing the eigenvalues and eigenvectors of a large sparse nonsymmetric matrix arises in many applications and can be a very computationally challenging problem. In this paper we propose the Augmented Block Householder Arnoldi (ABHA) method that combines the advantages of a block routine with an augmented Krylov routine. A public domain MATLAB code ahbeigs has been developed and numerical exp...
متن کامل