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

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

Certified And Fast Computations With Shallow Covariance Kernels

Daniel Kressner, Stefano Massei

Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random fields have gained ...

AMER INST MATHEMATICAL SCIENCES-AIMS2020

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

Phase retrieval in high dimensions: Statistical and computational phase transitions

Florent Gérard Krzakala, Lenka Zdeborová, Bruno Loureiro, Bruno Loureiro

We consider the phase retrieval problem of reconstructing a n -dimensional real or complex signal X ⋆ from m (possibly noisy) observations Y μ = | ∑ n i = 1 Φ μ i X ⋆ i / √ n | , for a large class of correlated real and complex random sensing matrices Φ , ...

Curran Associates, Inc.2020

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

Global eigenvalue distribution of matrices defined by the skew-shift

Marius Christopher Lemm

We consider large Hermitian matrices whose entries are defined by evaluating the exponential function along orbits of the skew-shift

\binom{j}{2} \omega+jy+x \mod 1

for irrational

\omega

. We prove that the eigenvalue distribution of these matrices conv ...

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

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

Kathryn Dianne Lund

We analyze an expansion of the generalized block Krylov subspace framework of [Electron.\ Trans.\ Numer.\ Anal., 47 (2017), pp. 100-126]. This expansion allows the use of low-rank modifications of the matrix projected onto the block Krylov subspace and con ...

MATHICSE2019

MATHICSE Technical Report : 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\times 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 ...

MATHICSE2019

Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization

Sebastian Urban Stich

We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive definite matrices i ...

2018

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

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

Certified And Fast Computations With Shallow Covariance Kernels

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

Phase retrieval in high dimensions: Statistical and computational phase transitions

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

Global eigenvalue distribution of matrices defined by the skew-shift

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

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

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization

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

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

Global eigenvalue distribution of matrices defined by the skew-shift

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

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

Certified And Fast Computations With Shallow Covariance Kernels

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

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Phase retrieval in high dimensions: Statistical and computational phase transitions

Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization