Publications related to Balancing sparse Hamiltonian eigenproblems

The Dimension of the Body in Higher Education: Matrix of Meanings in Students’ Diaries

In this paper, we attempt to show some consequences of bringing the body back into higher education, through the use of performing arts in the curricular context of scientific programs. We start by arguing that dominant traditions in higher education repro ...

2021

A fast spectral divide-and-conquer method for banded matrices

Daniel Kressner, Ana Susnjara

Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3):A1325-A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix with small bandwidth, w ...

WILEY2021

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

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

Daniel Kressner, Stefano Massei, Kathryn Dianne Lund

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

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Stefano Massei

Evaluating the action of a matrix function on a vector, that is

x=f(\mathcal M)v

, is an ubiquitous task in applications. When

\mathcal M

is large, one usually relies on Krylov projection methods. In this paper, we provide effective choices for the pole ...

2019

Fast hierarchical solvers for symmetric eigenvalue problems

Ana Susnjara

In this thesis we address the computation of a spectral decomposition for symmetric banded matrices. In light of dealing with large-scale matrices, where classical dense linear algebra routines are not applicable, it is essential to design alternative tech ...

EPFL2018

Solving Rank-Structured Sylvester And Lyapunov Equations

Stefano Massei

We consider the problem of efficiently solving Sylvester and Lyapunov equations of medium and large scale, in case of rank-structured data, i.e., when the coefficient matrices and the right-hand side have low-rank off-diagonal blocks. This comprises proble ...

SIAM PUBLICATIONS2018

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

Eigendecomposition-free Training of Deep Networks with Zero Eigenvalue-based Losses

Pascal Fua, Mathieu Salzmann, Zheng Dang, Kwang Moo Yi, Fei Wang, Yinlin Hu

Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be solved by ﬁnding the eigenvector corresponding to the smallest, or zero, eigenvalue of a matrix representing a linear sy ...

2018

New Approach to Identifying Critical Initial Conditions for Extreme Flood Simulations in a Semicontinuous Simulation Framework

Anton Schleiss, Javier García Hernández, Bettina Schaefli, Fränz Zeimetz, Guillaume Mathieu Artigue

Extreme flood simulation with synthetic extreme precipitation events raises unavoidable questions about the choice of initial conditions. State-of-the-art extreme flood estimation frameworks propose to address these questions with the help of semicontinuou ...

2018

Balancing sparse Hamiltonian eigenproblems

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The Dimension of the Body in Higher Education: Matrix of Meanings in Students’ Diaries

A fast spectral divide-and-conquer method for banded matrices

Complementary Asymptotically Sharp Estimates for Eigenvalue Means of Laplacians

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

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Fast hierarchical solvers for symmetric eigenvalue problems

Solving Rank-Structured Sylvester And Lyapunov Equations

A Householder-Based Algorithm For Hessenberg-Triangular Reduction

Eigendecomposition-free Training of Deep Networks with Zero Eigenvalue-based Losses

New Approach to Identifying Critical Initial Conditions for Extreme Flood Simulations in a Semicontinuous Simulation Framework

Solving Rank-Structured Sylvester And Lyapunov Equations

The Dimension of the Body in Higher Education: Matrix of Meanings in Students’ Diaries

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

Fast hierarchical solvers for symmetric eigenvalue problems

New Approach to Identifying Critical Initial Conditions for Extreme Flood Simulations in a Semicontinuous Simulation Framework

A fast spectral divide-and-conquer method for banded matrices

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

A Householder-Based Algorithm For Hessenberg-Triangular Reduction

Complementary Asymptotically Sharp Estimates for Eigenvalue Means of Laplacians

Eigendecomposition-free Training of Deep Networks with Zero Eigenvalue-based Losses