Spectra and Pseudospectra

By Lloyd N. Trefethen. 2020

725 citations recorded by the source corpus.

Subfields: Computer Graphics and Computer-Aided Design, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/86470d3a34538807fbee2f064b518a49164e2333

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In Computer Graphics and Computer-Aided Design

In Statistical and Nonlinear Physics

Citations in the corpus

Non-Hermitian Topological Phenomena: A Review (2022, methodology): “When H is diagonalizable, the theorem implies [4] σ (H) ⊆ σ(H) + ∆ κ(V ), (13) 10In numerical calculations, another equivalent definition [4] σ (H) = {z ∈ C | ||(z−H)−1|| > −1} is useful.”
Recent computational developments in Krylov subspace methods for linear systems (2007, methodology): “Different approaches have used the field of values and pseudospectrum as possibly more representative tools for highly non-normal matrices [91], [107], [315], [327], [328].”
Recent Progress on Truncated Toeplitz Operators (2011, background): “mmense topic. Instead, we merely refer the reader to several recent texts which analyze various aspects of this fascinating subject. The pseudospectral properties of Toeplitz matrices are explored in [98]. The asymptotic analysis of Toeplitz operators on H2 via large truncated Toeplitz matrices is t”
K-Theory and Pseudospectra for Topological Insulators (2015, methodology): “and not the convention with strict inequality, as in the excellent book [37] by Trefethen and Embree.”
Computing absolute and essential spectra using continuation (2007, background): “An additional difficulty arises when convective transport mechanisms cause linearized operators to be non-normal, leading to ill-conditioned eigenvalue problems where pseudo-spectra become relevant [18], and to sensitive dependence on boundary”
Dynamics and Control of Global Instabilities in Open-Flows: A Linearized Approach (2010, background): “only an infinite discrete countable set of eigenvalues exists [142].”
Finite Difference Methods for Differential Equations (2005, background): “See the recent book by Trefethen and Embree [TE05] for an in-depth discussion of pseudospectra with many examples of their use.”
On the hypergeometric matrix functions of two variables (2018, neutral): “3) The logarithmic norm of a matrix A ∈ Cr×r is defined as [11,12] μ(A) = lim h→0 ||I + hA|| − 1 h = max { z | z ∈ σ ( A + A∗ 2 )} .”
Finite difference methods for ordinary and partial differential equations - steady-state and time-dependent problems (2007, background): “46) and a proof of this can be found in [92].”
Around the circular law (2011, neutral): “See [150] for more.”
On the Solvability Complexity Index, the n-pseudospectrum and approximations of spectra of operators (2011, background): “For selected papers and books we consider to be important and related to the topic of this paper we refer to [9, 11, 10, 26, 32, 15, 14, 41, 19, 18, 28, 42, 47] for a functional analysis exposition and [50, 48, 25, 39] for a more applied mathematical treatment.”
Circular law theorem for random Markov matrices (2008, neutral): “Moreover, ε 1/n n → 1 and the limiting spectral distribution of B is the uniform distribution on the unit circle of the complex plane! In numerical analysis, the sensitivity of the spectrum is captured by the notion of pseudo-spectrum [49].”