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

New Results in Integer and Lattice Programming

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

,

b \in \Z^m

,

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

Recursive blocked algorithms for linear systems with Kronecker product structure

Daniel Kressner

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

A hierarchical preconditioner for wave problems in quasilinear complexity

Jan Sickmann Hesthaven, Boris Bonev

The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit the property th ...

2020

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

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: 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

Backpropagation-Friendly Eigendecomposition

Pascal Fua, Mathieu Salzmann, Zheng Dang, Wei Wang, Yinlin Hu

Eigendecomposition (ED) is widely used in deep networks. However, the backpropagation of its results tends to be numerically unstable, whether using ED directly or approximating it with the Power Iteration method, particularly when dealing with large matri ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2019

Method of displaying an image on a see-through display

Sabine Süsstrunk, Adrien Birbaumer, Martinus Bosch

The present invention concerns a method of displaying an image on a see-through display. The method comprises: obtaining (101) a first electromagnetic radiation matrix of an object, the first matrix comprising first matrix elements representing radiation i ...

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

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

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New Results in Integer and Lattice Programming

Recursive blocked algorithms for linear systems with Kronecker product structure

A hierarchical preconditioner for wave problems in quasilinear complexity

Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities

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

Backpropagation-Friendly Eigendecomposition

Method of displaying an image on a see-through display

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

Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities

A hierarchical preconditioner for wave problems in quasilinear complexity

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

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Method of displaying an image on a see-through display

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

New Results in Integer and Lattice Programming

Recursive blocked algorithms for linear systems with Kronecker product structure

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

Backpropagation-Friendly Eigendecomposition