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Eigenvalues, latent roots, proper values, characteristic valuesâ€”four synonyms for a set of numbers that provide much useful information about a matrix or operator. A huge amount of research has beenâ€¦ (More)

- Christopher A. Beattie, Mark Embree, John Rossi
- SIAM J. Matrix Analysis Applications
- 2004

The performance of Krylov subspace eigenvalue algorithms for large matrices can be measured by the angle between a desired invariant subspace and the Krylov subspace. We develop general bounds forâ€¦ (More)

- Mark Embree
- SIAM Review
- 2003

When solving large nonsymmetric systems of linear equations with the restarted GMRES algorithm, one is inclined to select a relatively large restart parameter in the hope of mimicking the full GMRESâ€¦ (More)

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions ofâ€¦ (More)

- Mark Embree
- 1999

Eigenvalues with the eigenvector condition number, the eld of values, and pseu-dospectra have all been suggested as the basis for convergence bounds for minimum residual Krylov subspace methodsâ€¦ (More)

- Mark Embree
- SIAM J. Matrix Analysis Applications
- 2009

The restarted Arnoldi algorithm, implemented in the ARPACK software library and MATLABâ€™s eigs command, is among the most common means of computing select eigenvalues and eigenvectors of a large,â€¦ (More)

- Christopher A. Beattie, Mark Embree, Danny C. Sorensen
- SIAM Review
- 2005

The convergence of Krylov subspace eigenvalue algorithms can be robustly measured by the angle the approximating Krylov space makes with a desired invariant subspace. This paper describes a new boundâ€¦ (More)

- Mark Embree, Lloyd N. Trefethen
- SIAM J. Scientific Computing
- 2001

Analysis of nonsymmetric matrix iterations based on eigenvalues can be misleading. In this paper, we discuss sixteen theorems involving Îµ-pseudospectra that each generalize a familiar eigenvalueâ€¦ (More)

- David Damanik, Mark Embree, ANTON GORODETSKI
- 2007

We study the spectrum of the Fibonacci Hamiltonian and prove upper and lower bounds for its fractal dimension in the large coupling regime. These bounds show that as Î» â†’ âˆž, dim(Ïƒ(HÎ»)) Â· log Î»â€¦ (More)

- Mark Embree, Lloyd N. Trefethen
- SIAM Review
- 1999

A method is described for the computation of the Greenâ€™s function in the complex plane corresponding to a set of K symmetrically placed polygons along the real axis. An important special case is aâ€¦ (More)