Publications related to Evaluating functions of positive-definite matrices using colored-noise thermostats

Efficient Learning of a Linear Dynamical System with Stability Guarantees

Daniel Kuhn, Wouter Jongeneel, Tobias Sutter

We propose a principled method for projecting an arbitrary square matrix to the non- convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an information-theoretic sense and ...

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

On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants

Daniel Kressner, Alice Cortinovis

Randomized trace estimation is a popular and well-studied technique that approximates the trace of a large-scale matrix B by computing the average of x(T) Bx for many samples of a random vector X. Often, B is symmetric positive definite (SPD) but a number ...

2021

Bootstrapping massive quantum field theories

Denis Karateev

We propose a new non-perturbative method for studying UV complete unitary quantum field theories (QFTs) with a mass gap in general number of spacetime dimensions. The method relies on unitarity formulated as positive semi-definiteness of the matrix of inne ...

SPRINGER2020

On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Daniel Kressner, Stefano Massei, Alice Cortinovis

The problem of finding a k x k submatrix of maximum volume of a matrix A is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of A. We show that such a submatrix can a ...

ELSEVIER SCIENCE INC2020

Efficient Distributed Transposition Of Large-Scale Multigraphs And High-Cardinality Sparse Matrices

Felix Schürmann, Bruno Ricardo Da Cunha Magalhães

Graph-based representations underlie a wide range of scientific problems. Graph connectivity is typically represented as a sparse matrix in the Compressed Sparse Row format. Large-scale graphs rely on distributed storage, allocating distinct subsets of row ...

2020

Kinetic Euclidean Distance Matrices

Martin Vetterli, Ivan Dokmanic, Puoya Tabaghi

Euclidean distance matrices (EDMs) are a major tool for localization from distances, with applications ranging from protein structure determination to global positioning and manifold learning. They are, however, static objects which serve to localize point ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Momentum space CFT correlators for Hamiltonian truncation

Matthew Thomas Walters

We consider Lorentzian CFT Wightman functions in momentum space. In particular, we derive a set of reference formulas for computing two- and three-point functions, restricting our attention to three-point functions where the middle operator (corresponding ...

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 ...

SIAM PUBLICATIONS2020

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

Evaluating functions of positive-definite matrices using colored-noise thermostats

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Efficient Learning of a Linear Dynamical System with Stability Guarantees

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

On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants

Bootstrapping massive quantum field theories

On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Efficient Distributed Transposition Of Large-Scale Multigraphs And High-Cardinality Sparse Matrices

Kinetic Euclidean Distance Matrices

Momentum space CFT correlators for Hamiltonian truncation

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Momentum space CFT correlators for Hamiltonian truncation

Kinetic Euclidean Distance Matrices

Efficient Learning of a Linear Dynamical System with Stability Guarantees

On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Efficient Distributed Transposition Of Large-Scale Multigraphs And High-Cardinality Sparse Matrices

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

Bootstrapping massive quantum field theories