Publications associées à Inverse iteration

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

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Daniel Kressner, Ivana Sain Glibic

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are ...

SPRINGER2023

Weakly nonlinear evolution of stochastically driven non-normal systems

François Gallaire, Edouard Boujo, Yves-Marie François Ducimetière

We consider nonlinear dynamical systems driven by stochastic forcing. It has been largely evidenced in the literature that the linear response of non-normal systems (e.g. fluid flows) may exhibit a large variance amplification, even in a linearly stable re ...

2022

A Householder-Based Algorithm For Hessenberg-Triangular Reduction

Daniel Kressner, Zvonimir Bujanovic

The QZ algorithm for computing eigenvalues and eigenvectors of a matrix pencil A - lambda B requires that the matrices first be reduced to Hessenberg-triangular (HT) form. The current method of choice for HT reduction relies entirely on Givens rotations re ...

SIAM PUBLICATIONS2018

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

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

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

Optimization of mesh hierarchies in multilevel Monte Carlo samplers

Fabio Nobile, Erik Gustaf Bogislaw Von Schwerin

We perform a general optimization of the parameters in the multilevel Monte Carlo (MLMC) discretization hierarchy based on uniform discretization methods with general approximation orders and computational costs. We optimize hierarchies with geometric and ...

2016

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Inverse iteration

A mixed precision LOBPCG algorithm

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Weakly nonlinear evolution of stochastically driven non-normal systems

Eigenmode Analysis in Plasmonics: Application to Second Harmonic Generation and Electron Energy Loss Spectroscopy

A Householder-Based Algorithm For Hessenberg-Triangular Reduction

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

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

Subspace Acceleration For Large-Scale Parameter-Dependent Hermitian Eigenproblems

Optimization of mesh hierarchies in multilevel Monte Carlo samplers

Low-rank methods for parameter-dependent eigenvalue problems and matrix equations

Graph Chatbot

Chattez avec Graph Search

A mixed precision LOBPCG algorithm

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Weakly nonlinear evolution of stochastically driven non-normal systems

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

Optimization of mesh hierarchies in multilevel Monte Carlo samplers

Low-rank methods for parameter-dependent eigenvalue problems and matrix equations

Eigenmode Analysis in Plasmonics: Application to Second Harmonic Generation and Electron Energy Loss Spectroscopy

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

Subspace Acceleration For Large-Scale Parameter-Dependent Hermitian Eigenproblems

A Householder-Based Algorithm For Hessenberg-Triangular Reduction