Publications related to Nonlinear Eigenvalue Problems With Specified Eigenvalues

Related publications (33)

Harmonic Stability Analysis of Microgrids with Converter-Interfaced Distributed Energy Resources, Part I: Modelling and Theoretical Foundations

Mario Paolone, Andreas Martin Kettner, Johanna Kristin Maria Becker

This paper proposes a method for the Harmonic Stability Assessment (HSA) of power systems with a high share of Converter-Interfaced Distributed Energy Resources (CIDERs). To this end, the Harmonic State-Space (HSS) model of a generic power system is formul ...

Institute of Electrical and Electronics Engineers (IEEE)2025

Randomized Nyström Approximation of Non-negative Self-Adjoint Operators

Daniel Kressner

The randomized singular value decomposition (SVD) has become a popular approach to computing cheap, yet accurate, low-rank approximations to matrices due to its efficiency and strong theoretical guarantees. Recent work by Boullé and Townsend [Found. Comput ...

Society for Industrial & Applied Mathematics (SIAM)2025

RANDOMIZED JOINT DIAGONALIZATION OF SYMMETRIC

Daniel Kressner, Haoze He

Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD) for performing t ...

Siam Publications2024

Intermediate Address Space: virtual memory optimization of heterogeneous architectures for cache-resident workloads

Qunyou Liu, David Atienza Alonso, Marina Zapater Sancho, Darong Huang, Luis Maria Costero Valero

The increasing demand for computing power and the emergence of heterogeneous computing architectures have driven the exploration of innovative techniques to address current limitations in both the compute and memory subsystems. One such solution is the use ...

2024

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Ivana Sain Glibic, Daniel Kressner

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

Entrepreneurial Opportunities and Threats in the Era of Grand Societal Challenges

Enrico Bergamini

We live in an era defined by attempts to grapple with an ever-expanding array of grand societal challenges (GCs). These challenges comprise transformational social and environmental issues, such as environmental degradation and global pandemics, and the cr ...

EPFL2023

Homogenization results for the generator of multiscale Langevin dynamics in weighted Sobolev spaces

Andrea Zanoni

We study the homogenization of the Poisson equation with a reaction term and of the eigenvalue problem associated to the generator of multiscale Langevin dynamics. Our analysis extends the theory of two-scale convergence to the case of weighted Sobolev spa ...

OXFORD UNIV PRESS2023

Rebooting Virtual Memory with Midgard

Siddharth Gupta

Virtual Memory (VM) is a critical programming abstraction that is widely used in various modern computing platforms. With the rise of datacenter computing and birth of planet-scale online services, the semantic and capacity requirements from memory have ev ...

EPFL2023

TimeEvolver: A program for time evolution with improved error bound

Sebastian Zell

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

ELSEVIER2022

Expanding biochemical knowledge and illuminating metabolic dark matter with ATLASx

Vassily Hatzimanikatis, Jasmin Maria Hafner, Anastasia Sveshnikova

Metabolic "dark matter" describes currently unknown metabolic processes, which form a blind spot in our general understanding of metabolism and slow down the development of biosynthetic cell factories and naturally derived pharmaceuticals. Mapping the dark ...

Nature Portfolio2022

Second-order adjoint-based sensitivity for hydrodynamic stability and control

Edouard Boujo

Adjoint-based sensitivity analysis is routinely used today to assess efficiently the effect of open-loop control on the linear stability properties of unstable flows. Sensitivity maps identify regions where small-amplitude control is the most effective, i. ...

Cambridge University Press2021

Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval

Fabio Nobile, Yoshihito Kazashi

An existence result is presented for the dynamical low rank (DLR) approximation for random semi-linear evolutionary equations. The DLR solution approximates the true solution at each time instant by a linear combination of products of deterministic and sto ...

2021

Robust Differentiable SVD

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

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

Complementary Asymptotically Sharp Estimates for Eigenvalue Means of Laplacians

Joachim Stubbe, Luigi Provenzano

We present asymptotically sharp inequalities, containing a 2nd term, for the Dirichlet and Neumann eigenvalues of the Laplacian on a domain, which are complementary to the familiar Berezin-Li-Yau and Kroger inequalities in the limit as the eigenvalues tend ...

OXFORD UNIV PRESS2021

Mathematical and numerical models for the cardiac electromechanical function

Alfio Quarteroni, Francesco Regazzoni

This paper deals with the mathematical model that describes the function of the human heart. More specifically, it addresses the equations that express the electromechanical process, that is the mechanical deformation (contraction and relaxation) of the he ...

EUROPEAN MATHEMATICAL SOC-EMS2021

Bifurcation points of a singular boundary-value problem on (0,1)

Charles Stuart

Following earlier work on some special cases [17,11] and on the analogous problem in higher dimensions [10,20], we make a more thorough investigation of the bifurcation points for a nonlinear boundary value problem of the form -{A(x)u' (x)}'.= f (lambda, x ...

Academic Press Inc Elsevier Science2016

On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems

Daniel Kressner, André Uschmajew

Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems and eigenvalue p ...

Elsevier Science Inc2016

Compress-and-restart block Krylov subspace methods for Sylvester matrix equations

Kathryn Dianne Lund, Daniel Kressner, Stefano Massei

Block Krylov subspace methods (KSMs) comprise building blocks in many state-of-the-art solvers for large-scale matrix equations as they arise, for example, from the discretization of partial differential equations. While extended and rational block Krylov ...

2020

Accurate, Stable and Efficient Modal Calculations of Photoelectrically Useful Absorption in Lamellar Metallic and Semiconductor Diffraction Gratings

David Isaak Gablinger

Solar energy has seen tremendous advances in the past years. For thin film photovoltaics, which use less of the expensive semiconductor materials, insufficient light absorption can be a limiting factor. It is hoped that by using diffractive optics to impro ...

EPFL2016

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

Daniel Kressner, Stefano Massei

Matrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile tool to develop fast algorithms for addressing large-scale problems. While existing software packages for such matrices often focus on linear systems, t ...

SIAM PUBLICATIONS2020