Publications related to MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

Construction of optimal spectral methods in phase retrieval

Florent Gérard Krzakala, Lenka Zdeborová

We consider the phase retrieval problem, in which the observer wishes to recover a n-dimensional real or complex signal X⋆ from the (possibly noisy) observation of |ΦX⋆|, in which Φ is a matrix of size m×n. We consider a \emph{high-dimensional} setting whe ...

2021

Low-Rank Updates Of Matrix Functions Ii: Rational Krylov Methods

Daniel Kressner, Alice Cortinovis, Marcel Schweitzer

This work develops novel rational Krylov methods for updating a large-scale matrix function f(A) when A is subject to low-rank modifications. It extends our previous work in this context on polynomial Krylov methods, for which we present a simplified conve ...

SIAM PUBLICATIONS2021

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

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

Evaporation of Metals during the Thermal Treatment of Oxide Nanomaterials in Cellulose-Based Matrices

Christian Ludwig, Mohamed Tarik

Like conventional material products, waste is the last stage of the life cycle of engineered nanomaterials, which are then incinerated or stabilized before disposal. However, because of their special physical characteristics, the fate of the thermally trea ...

2020

Point, Plane, Set, Match! Winning the Echo Grand SLAM

Miranda Krekovic

Some of the most important and challenging problems in science are inverse problems. They allow us to understand phenomena that cannot be measured directly. Inverse problems might not always have a unique or stable solution, or might not have any solution ...

EPFL2020

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

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

The S-matrix bootstrap. Part III: higher dimensional amplitudes

Jonathan Campbell Toledo

We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 3+1 dimensions due to crossing symmetry, analyticity and unitarity. We extremize cubic couplings, quartic couplings and scattering lengths relevant for the ela ...

SPRINGER2019

Spectral gaps of frustration-free spin systems with boundary

Marius Christopher Lemm

In quantum many-body systems, the existence of a spectral gap above the ground state has far-reaching consequences. In this paper, we discuss “finite-size” criteria for having a spectral gap in frustration-free spin systems and their applications. We exten ...

2019

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

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Construction of optimal spectral methods in phase retrieval

Low-Rank Updates Of Matrix Functions Ii: Rational Krylov Methods

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities

Evaporation of Metals during the Thermal Treatment of Oxide Nanomaterials in Cellulose-Based Matrices

Point, Plane, Set, Match! Winning the Echo Grand SLAM

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

hm-toolbox: Matlab software for HODLR and HSS matrices

The S-matrix bootstrap. Part III: higher dimensional amplitudes

Spectral gaps of frustration-free spin systems with boundary

Construction of optimal spectral methods in phase retrieval

Low-Rank Updates Of Matrix Functions Ii: Rational Krylov Methods

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

hm-toolbox: Matlab software for HODLR and HSS matrices

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities

Evaporation of Metals during the Thermal Treatment of Oxide Nanomaterials in Cellulose-Based Matrices

Point, Plane, Set, Match! Winning the Echo Grand SLAM

The S-matrix bootstrap. Part III: higher dimensional amplitudes

Spectral gaps of frustration-free spin systems with boundary