Publications related to Spectrum of a matrix

The locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm is a popular approach for computing a few smallest eigenvalues and the corresponding eigenvectors of a large Hermitian positive definite matrix A. In this work, we propose a mix ...

SPRINGER2023

Failure and success of the spectral bias prediction for Laplace Kernel Ridge Regression: the case of low-dimensional data

Matthieu Wyart, Umberto Maria Tomasini, Antonio Sclocchi

Recently, several theories including the replica method made predictions for the generalization error of Kernel Ridge Regression. In some regimes, they predict that the method has a 'spectral bias': decomposing the true function f* on the eigenbasis of the ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2022

Model order reduction for compressible flows solved using the discontinuous Galerkin methods

Jan Sickmann Hesthaven

Projection-based reduced order models (ROM) based on the weak form and the strong form of the discontinuous Galerkin (DG) method are proposed and compared for shock-dominated problems. The incorporation of dissipation components of DG in a consistent manne ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Robust Differentiable SVD

Pascal Fua, Mathieu Salzmann, Zheng Dang, Wei Wang, Yinlin Hu

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) ...

2021

Backpropagation-Friendly Eigendecomposition

Pascal Fua, Mathieu Salzmann, Zheng Dang, Wei Wang, Yinlin Hu

Eigendecomposition (ED) is widely used in deep networks. However, the backpropagation of its results tends to be numerically unstable, whether using ED directly or approximating it with the Power Iteration method, particularly when dealing with large matri ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2019

A generalized definition of reactivity for ecological systems and the problem of transient species dynamics

Andrea Rinaldo, Lorenzo Mari, Marino Gatto

Perturbations to an ecosystem's steady state can trigger transient responses of great ecological relevance. Asymptotic stability determines whether a generic perturbation will fade out in the long run, but falls short of characterizing the dynamics imme ...

Wiley2017

Conformal Mapping of Impedance Stability Models for System-Level Dynamics Assessments

Drazen Dujic, Francisco Daniel Freijedo Fernández, Uzair Javaid

Impedance stability methods are suitable for assessing the dynamics of power converters controllers, but also for ac/dc microgrids system level studies. This work proposes the combination of impedance modeling and conformal mapping for the identification o ...

2017

When Slepian Meets Fiedler: Putting a Focus on the Graph Spectrum

Dimitri Nestor Alice Van De Ville, Maria Giulia Preti, Robin Jonathan Demesmaeker

The study of complex systems greatly benefits from graph models and their analysis. In particular, the eigendecomposition of the graph Laplacian lets emerge properties of global organization from local interactions; e.g., the Fiedler vector has the smalles ...

Institute of Electrical and Electronics Engineers2017

Subspace Acceleration For Large-Scale Parameter-Dependent Hermitian Eigenproblems

Daniel Kressner, Petar Sirkovic

This work is concerned with approximating the smallest eigenvalue of a parameter-dependent Hermitian matrix A(mu) for many parameter values mu in a domain D subset of R-P. The design of reliable and efficient algorithms for addressing this task is of impor ...

Siam Publications2016

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Spectrum of a matrix

A mixed precision LOBPCG algorithm

Failure and success of the spectral bias prediction for Laplace Kernel Ridge Regression: the case of low-dimensional data

Model order reduction for compressible flows solved using the discontinuous Galerkin methods

Robust Differentiable SVD

Backpropagation-Friendly Eigendecomposition

A generalized definition of reactivity for ecological systems and the problem of transient species dynamics

Conformal Mapping of Impedance Stability Models for System-Level Dynamics Assessments

When Slepian Meets Fiedler: Putting a Focus on the Graph Spectrum

Subspace Acceleration For Large-Scale Parameter-Dependent Hermitian Eigenproblems

MATHICSE Technical Report : A reduced basis approach to large-scale pseudospectra computation

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Chat with Graph Search

A mixed precision LOBPCG algorithm

Failure and success of the spectral bias prediction for Laplace Kernel Ridge Regression: the case of low-dimensional data

Model order reduction for compressible flows solved using the discontinuous Galerkin methods

Robust Differentiable SVD

A generalized definition of reactivity for ecological systems and the problem of transient species dynamics

Backpropagation-Friendly Eigendecomposition

Conformal Mapping of Impedance Stability Models for System-Level Dynamics Assessments

When Slepian Meets Fiedler: Putting a Focus on the Graph Spectrum

MATHICSE Technical Report : A reduced basis approach to large-scale pseudospectra computation

Subspace Acceleration For Large-Scale Parameter-Dependent Hermitian Eigenproblems