Author
Mark Embree
Other affiliations: Rice University, University of Oxford
Bio: Mark Embree is an academic researcher from Virginia Tech. The author has contributed to research in topics: Eigenvalues and eigenvectors & Generalized minimal residual method. The author has an hindex of 17, co-authored 57 publications receiving 2356 citations. Previous affiliations of Mark Embree include Rice University & University of Oxford.
Papers published on a yearly basis
Papers
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01 Jan 2005
TL;DR: In this article, the authors introduce pseudospectra and non-normal matrices, and describe the behavior of nonsymmetric eigenproblems in non-hermitian systems.
Abstract: spectra and pseudospectra springerlink. spectra and pseudospectra the behavior of nonnormal. spectra and pseudospectra the behavior of nonnormal. spectra and pseudospectra the behavior of nonnormal. on n ? pseudospectra of operators on banach spaces. phd course on pseudospectra aalb universitet. nonhermitian systems and pseudospectra. spectra and pseudospectra the behavior of nonnormal. spectra and pseudospectra the behavior of nonnormal. pseudospectrum scholarpedia. spectra and pseudospectra the behavior of nonnormal. spectra and pseudospectra the behavior of nonnormal. customer reviews spectra and pseudospectra. spectra and pseudospectra request pdf. an introduction to pseudo spectra and non normal matrices. spectra and pseudospectra gbv. pseudospectrum. spectra and pseudospectra the behavior of nonnormal. ???? spectra and pseudospectra the behavior of nonnormal. spectra and pseudospectra the behavior of nonnormal. mark embree lloyd n trefethen abebooks. spectra and pseudospectra the behavior of nonnormal. eigtool a graphical tool for nonsymmetric eigenproblems. spectra and pseudospectra the behavior of nonnormal. universality of non normality in real arxiv vanity. spectra and pseudospectra lloyd n trefethen mark embree. spectra and pseudospectra the behavior of nonnormal. pseudospectra and nonnormal dynamical systems. booksavages. review of spectra and pseudospectra the behavior of. spectra pseudospectra and localization for random. spectra and pseudospectra of block toeplitz matrices. lecture notes on spectra and pseudospectra of matrices and. structure and dynamical behavior of non normal networks. lecture 2 nonnormality and pseudospectra. spectra and pseudospectra the behavior of nonnormal. numerical range for some plex upper triangular matrices. spectra and pseudospectra the behavior of nonnormal. spectra and pseudospectra the behavior of nonnormal. mark embree virginia tech. spectra and pseudospectra princeton university press. bookask?????? ??????????. spectra and pseudospectra the behavior of nonnormal. pseudospectra and inverse pseudospectra springerlink. review of spectra and pseudospectra the behavior of. nick trefethen. pseudospectrum mathematical garden
1,463 citations
TL;DR: In this article, the authors studied the spectrum of the Fibonacci Hamiltonian and proved upper and lower bounds for its fractal dimension in the large coupling regime and showed that it converges to an explicit constant.
Abstract: 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 $$\lambda \to \infty, {\rm dim} (\sigma(H_\lambda)) \cdot {\rm log} \lambda$$
converges to an explicit constant, $${\rm log}(1+\sqrt{2})\approx 0.88137$$
. We also discuss consequences of these results for the rate of propagation of a wavepacket that evolves according to Schrodinger dynamics generated by the Fibonacci Hamiltonian.
100 citations
TL;DR: A survey of results on self-adjoint operators with Sturmian potentials can be found in this article, where the authors focus their attention on the one-dimensional case, and in particular on several key examples.
Abstract: We survey results that have been obtained for self-adjoint operators, and especially Schrodinger operators, associated with mathematical models of quasicrystals. After presenting general results that hold in arbitrary dimensions, we focus our attention on the one-dimensional case, and in particular on several key examples. The most prominent of these is the Fibonacci Hamiltonian, for which much is known by now and to which an entire section is devoted here. Other examples that are discussed in detail are given by the more general class of Schrodinger operators with Sturmian potentials. We put some emphasis on the methods that have been introduced quite recently in the study of these operators, many of them coming from hyperbolic dynamics. We conclude with a multitude of numerical calculations that illustrate the validity of the known rigorous results and suggest conjectures for further exploration.
89 citations
TL;DR: This work analyzes the role of this term in the LDG discretization of the Maxwell curl–curl operator, demonstrating that the stabilization parameter can be used to split the spectrum into two sections.
84 citations
TL;DR: Two simple examples are presented where GM RES(1) converges exactly in three iterations, while GMRES(2) stagnates, revealing that GMRES (1) convergence can be extremely sensitive to small changes in the initial residual.
Abstract: 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 GMRES process. Surprisingly, cases exist where small values of the restart parameter yield convergence in fewer iterations than larger values. Here, two simple examples are presented where GMRES(1) converges exactly in three iterations, while GMRES(2) stagnates. One of these examples reveals that GMRES(1) convergence can be extremely sensitive to small changes in the initial residual.
80 citations
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01 Jan 2003
2,810 citations
2,618 citations
1,524 citations
TL;DR: Over the past decade considerable progress has been made towards the numerical solution of large-scale eigenvalue problems, particularly for nonsymmetric matrices, and the methods and software that have led to these advances are surveyed.
Abstract: Over the past decade considerable progress has been made towards the numerical solution of large-scale eigenvalue problems, particularly for nonsymmetric matrices. Krylov methods and variants of subspace iteration have been improved to the point that problems of the order of several million variables can be solved. The methods and software that have led to these advances are surveyed.
1,124 citations
TL;DR: The intent of this document is to provide an introduction to modal analysis that is accessible to the larger fluid dynamics community and presents a brief overview of several of the well-established techniques.
Abstract: Simple aerodynamic configurations under even modest conditions can exhibit complex flows with a wide range of temporal and spatial features. It has become common practice in the analysis of these flows to look for and extract physically important features, or modes, as a first step in the analysis. This step typically starts with a modal decomposition of an experimental or numerical dataset of the flowfield, or of an operator relevant to the system. We describe herein some of the dominant techniques for accomplishing these modal decompositions and analyses that have seen a surge of activity in recent decades [1–8]. For a nonexpert, keeping track of recent developments can be daunting, and the intent of this document is to provide an introduction to modal analysis that is accessible to the larger fluid dynamics community. In particular, we present a brief overview of several of the well-established techniques and clearly lay the framework of these methods using familiar linear algebra. The modal analysis techniques covered in this paper include the proper orthogonal decomposition (POD), balanced proper orthogonal decomposition (balanced POD), dynamic mode decomposition (DMD), Koopman analysis, global linear stability analysis, and resolvent analysis.
1,110 citations