Distribution of mathematical software via electronic mail
Communications of the ACM
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
A relative backward perturbation theorem for the Eigenvalue problem
Numerische Mathematik
Large-scale complex eigenvalue problems
Journal of Computational Physics
Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
Computing selected eigenvalues of sparse unsymmetric matrices using subspace iteration
ACM Transactions on Mathematical Software (TOMS)
An invert-free Arnoldi method for computing interior eigenpairs of large matrices
International Journal of Computer Mathematics
Deflated block Krylov subspace methods for large scale eigenvalue problems
Journal of Computational and Applied Mathematics
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Arnoldi methods can be more effective than subspace iterationmethods for computing the dominant eigenvalues of a large, sparse, real,unsymmetric matrix. A code, EB12, for thesparse, unsymmetric eigenvalue problem based on a subspace iterationalgorithm, optionally combined with Chebychev acceleration, has recentlybeen described by Duff and Scott and is included in the HarwellSubroutine Library. In this article we consider variants of the methodof Arnoldi and discuss the design and development of a code to implementthese methods. The new code, which is calledEB13, offers the user the choice of abasic Arnoldi algorithm, an Arnoldi algorithm with Chebychevacceleration, and a Chebychev preconditioned Arnoldi algorithm. Eachmethod is available in blocked and unblocked form. The code may be usedto compute either the rightmost eigenvalues, the eigenvalues of largestabsolute value, or the eigenvalues of largest imaginary part. Theperformance of each option in the EB13package is compared with that of subspace iteration on a range of testproblems, and on the basis of the results, advice is offered to the useron the appropriate choice of method.—Author's Abstract