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Concept

Coefficient matrix

Publications associées (12)

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

The time-dependent expected reward and deviation matrix of a finite QBD process

Sophie Myriam Hautphenne

Deriving the time-dependent expected reward function associated with a continuous-time Markov chain involves the computation of its transient deviation matrix. In this paper we focus on the special case of a finite quasi-birth-and-death (QBD) process, moti ...

ELSEVIER SCIENCE INC2019

On quadratic matrix equations with infinite size coefficients encountered in QBD stochastic processes

Stefano Massei

Matrix equations of the kind A(1)X(2)+A(0)X+A(-1)=X, where both the matrix coefficients and the unknown are semi-infinite matrices belonging to a Banach algebra, are considered. These equations, where coefficients are quasi-Toeplitz matrices, are encounter ...

WILEY2018

Solving Rank-Structured Sylvester And Lyapunov Equations

Stefano Massei

We consider the problem of efficiently solving Sylvester and Lyapunov equations of medium and large scale, in case of rank-structured data, i.e., when the coefficient matrices and the right-hand side have low-rank off-diagonal blocks. This comprises proble ...

SIAM PUBLICATIONS2018

Ultrafast ultrasound imaging as an inverse problem: Matrix-free sparse image reconstruction

Jean-Philippe Thiran, Yves Wiaux, Rafael Eduardo Carrillo Rangel, Marcel Arditi, Adrien Georges Jean Besson, Dimitris Perdios, Florian Martinez

Conventional ultrasound (US) image reconstruction methods rely on delay-and-sum (DAS) beamforming, which is a relatively poor solution of the image reconstruction problem. An alternative to DAS consists in using iterative techniques which require both an a ...

2017

Extension complexity of stable set polytopes of bipartite graphs

Yuri Faenza, Manuel Francesco Aprile

The extension complexity xc(P) of a polytope P is the minimum number of facets of a polytope that affinely projects to P. Let G be a bipartite graph with n vertices, m edges, and no isolated vertices. Let STAB(G) be the convex hull of the stable sets of G. ...

Springer2017

Low-rank methods for parameter-dependent eigenvalue problems and matrix equations

Petar Sirkovic

The focus of this thesis is on developing efficient algorithms for two important problems arising in model reduction, estimation of the smallest eigenvalue for a parameter-dependent Hermitian matrix and solving large-scale linear matrix equations, by extra ...

EPFL2016

Truncated low-rank methods for solving general linear matrix equations

Daniel Kressner, Petar Sirkovic

This work is concerned with the numerical solution of large-scale linear matrix equations A1XB1T++AKXBKT=C. The most straightforward approach computes XRmxn from the solution of an mn x mn linear system, typically limiting the feasible values of m,n to a f ...

Wiley-Blackwell2015

Ad Hoc Microphone Array Calibration: Euclidean Distance Matrix Completion Algorithm and Theoretical Guarantees

Hervé Bourlard, Philip Neil Garner, Afsaneh Asaei, Reza Parhizkar, Mohammadjavad Taghizadeh

This paper addresses the problem of ad hoc microphone array calibration where only partial information about the distances between the microphones is available. We construct a matrix consisting of the pairwise distances and propose to estimate the missing ...

2015