Spectra and pseudospectra : the behavior of nonnormal matrices and operators

By Lloyd N. Trefethen, M. Embree. 2005

1,669 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/0ec43db4db4a44a9453fd09997870e202ab0e512

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Input–output analysis, model reduction and control of the flat-plate boundary layer (2009, background): “The operator satisfies the properties T(t + s) = T(t)T(s), T(0) = I and can be considered a semi-group (see, e.g. Pazy 1983; Trefethen & Embree 2005) of the form exp(At)† with the infinitesimal generator Au = lim δt→0 T(δt)u − u δt .”
DECAY BOUNDS AND ( ) ALGORITHMS FOR APPROXIMATING FUNCTIONS OF SPARSE MATRICES (2007, background): “In particular, when A is highly non-normal (in the sense that κ(X) ≫ 1) the bound can be a severe overestimate of the actual size of the elements of f(A), and in this case other tools, such as for example pseudospectra, may be better suited to characterize the actual decay behavior; see [78, 79].”
Balanced amplification: a new mechanism of selective amplification of neural activity patterns (2009, positive): “[1993], which led us to Trefethen and Embree [2005] and thus to connect our results to the dynamics of non-normal matrices, and Mark Goldman and Surya Ganguli for remarkably collegial relationships as we all independently discovered the joys of non-normal connection matrices.”
A critical-layer framework for turbulent pipe flow (2010, methodology): “Waleffe (1997, 2001, 2003) followed a different approach, developing exact solutions of the Navier-Stokes equations that give rise to unstable coherent structures which they propose form the foundations of transitional flow and near-wall turbulence. Subsequently there has been much interest in the i”
Memory without Feedback in a Neural Network (2009, methodology): “For a complementary approach (pseu-dospectral analysis [Trefethen and Embree, 2005]) to analyzing the functionally feedforward networks, see the Supplemental Experimental Procedures.”
Enhanced Dissipation, Hypoellipticity, and Anomalous Small Noise Inviscid Limits in Shear Flows (2015, background): “The work [22] studies the spectral and pseudo-spectral properties (see [46] or Section 4) of the harmonic oscillator with an additional large, complex potential.”
Recent Progress on Truncated Toeplitz Operators (2011, background): “The pseudospectral properties of Toeplitz matrices are explored in [100].”
Resolvent-analysis-based design of airfoil separation control (2018, background): “By introducing the similarity transformation of Hq̄ 7→ Hq̄,W = W 1 2 Hq̄W− 1 2 , the energy norm for Hq̄ can be handled within the 2-norm framework for Hq̄,W (Trefethen & Embree 2005).”
Nonmodal Stability Theory (2007, background): “This phenomenon is referred to as pseudoresonance (Trefethen et al. 1993).”
Modal Analysis of Fluid Flows: Applications and Outlook (2019, methodology): “. The evolution of the energy of the system for this trajectory will be shown in Fig.7. Note that transient growth may be formally related to pseudospectral/resolvent analysis via the Kreiss constant [76], as discussed in the context of channel ow in [70,75]. 12 of37 American Institute of Aeronautic”