Publications related to MATHICSE Technical Report: Block Krylov subspace methods for functions of matrices II: Modified block FOM

Recursive blocked algorithms for linear systems with Kronecker product structure

Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to higher-dimensional variants of g ...

SPRINGER2020

Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities

Marius Christopher Lemm

The Lyapunov exponent characterizes the asymptotic behavior of long matrix products. Recognizing scenarios where the Lyapunov exponent is strictly positive is a fundamental challenge that is relevant in many applications. In this work we establish a novel ...

2020

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 ...

2019

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

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

On multivariate trace inequalities of Sutter, Berta, and Tomamichel

Marius Christopher Lemm

We consider a family of multivariate trace inequalities recently derived by Sutter, Berta, and Tomamichel. These inequalities generalize the Golden-Thompson inequality and Lieb’s triple matrix inequality to an arbitrary number of matrices in a way that fea ...

2018

MATHICSE Technical Report : Low-rank updates and a divideand- conquer method for linear matrix equations

Daniel Kressner, Stefano Massei

Linear matrix equations, such as the Sylvester and Lyapunov equations, play an important role in various applications, including the stability analysis and dimensionality reduction of linear dynamical control systems and the solution of partial differentia ...

MATHICSE2017

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

Petar Sirkovic

The focus of this thesis is on developing efficient algorithms for two important problems arising in model reduction, estimation of the smallest eigenvalue for a parameter-dependent Hermitian matrix and solving large-scale linear matrix equations, by extra ...

EPFL2016

A Family of Smooth and Interpolatory Basis Functions for Parametric Curve and Surface Representation

Michaël Unser, Daniel Andreas Schmitter, Ricard Delgado Gonzalo

Interpolatory basis functions are helpful to specify parametric curves or surfaces that can be modified by simple user-interaction. Their main advantage is a characterization of the object by a set of control points that lie on the shape itself (i.e., curv ...

2016

Memory-efficient Arnoldi algorithms for linearizations of matrix polynomials in Chebyshev basis

Daniel Kressner

Novel memory-efficient Arnoldi algorithms for solving matrix polynomial eigenvalue problems are presented. More specifically, we consider the case of matrix polynomials expressed in the Chebyshev basis, which is often numerically more appropriate than the ...

Wiley-Blackwell2014

MATHICSE Technical Report: Block Krylov subspace methods for functions of matrices II: Modified block FOM

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Recursive blocked algorithms for linear systems with Kronecker product structure

Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities

hm-toolbox: Matlab software for HODLR and HSS matrices

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

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

On multivariate trace inequalities of Sutter, Berta, and Tomamichel

MATHICSE Technical Report : Low-rank updates and a divideand- conquer method for linear matrix equations

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

A Family of Smooth and Interpolatory Basis Functions for Parametric Curve and Surface Representation

Memory-efficient Arnoldi algorithms for linearizations of matrix polynomials in Chebyshev basis

hm-toolbox: Matlab software for HODLR and HSS matrices

Recursive blocked algorithms for linear systems with Kronecker product structure

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Memory-efficient Arnoldi algorithms for linearizations of matrix polynomials in Chebyshev basis

On multivariate trace inequalities of Sutter, Berta, and Tomamichel

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

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

MATHICSE Technical Report : Low-rank updates and a divideand- conquer method for linear matrix equations

A Family of Smooth and Interpolatory Basis Functions for Parametric Curve and Surface Representation

Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities