Publications associées à Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

Siam Publications2024

Preconditioning techniques for generalized Sylvester matrix equations

Yannis Dirk Voet

Sylvester matrix equations are ubiquitous in scientific computing. However, few solution techniques exist for their generalized multiterm version, as they recently arose in stochastic Galerkin finite element discretizations and isogeometric analysis. In th ...

2023

IMPROVED VARIANTS OF THE HUTCH plus plus ALGORITHM FOR TRACE ESTIMATION

Daniel Kressner, Ulf David Persson, Alice Cortinovis

This paper is concerned with two improved variants of the Hutch++ algorithm for estimating the trace of a square matrix, implicitly given through matrix-vector products. Hutch++ combines randomized low-rank approximation in a first phase with stochastic tr ...

SIAM PUBLICATIONS2022

Iterative refinement of Schur decompositions

Daniel Kressner, Zvonimir Bujanovic

The Schur decomposition of a square matrix A is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following task: Compute a (m ...

SPRINGER2022

Fast deterministic and randomized algorithms for low-rank approximation, matrix functions, and trace estimation

Alice Cortinovis

In this thesis we propose and analyze algorithms for some numerical linear algebra tasks: finding low-rank approximations of matrices, computing matrix functions, and estimating the trace of matrices.In the first part, we consider algorithms for building l ...

EPFL2022

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

Daniel Kressner, Stefano Massei, Alice Cortinovis

This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for performing low-rank up ...

SIAM PUBLICATIONS2022

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

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 : 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

Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data

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SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

Preconditioning techniques for generalized Sylvester matrix equations

IMPROVED VARIANTS OF THE HUTCH plus plus ALGORITHM FOR TRACE ESTIMATION

Iterative refinement of Schur decompositions

Fast deterministic and randomized algorithms for low-rank approximation, matrix functions, and trace estimation

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

Bootstrapping massive quantum field theories

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

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

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

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

Iterative refinement of Schur decompositions

Bootstrapping massive quantum field theories

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

IMPROVED VARIANTS OF THE HUTCH plus plus ALGORITHM FOR TRACE ESTIMATION

Fast deterministic and randomized algorithms for low-rank approximation, matrix functions, and trace estimation

Preconditioning techniques for generalized Sylvester matrix equations

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

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

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