Publications related to MATHICSE Technical Report : Low-rank updates and divide-andconquer methods for quadratic matrix equations

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

ELSEVIER SCIENCE INC2023

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

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

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

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

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

Matrix recovery from bilinear and quadratic measurements

Martin Vetterli, Adam James Scholefield, Michalina Wanda Pacholska, Karen Adam

Matrix (or operator) recovery from linear measurements is a well-studied problem. However, there are situations where only bilinear or quadratic measurements are available. A bilinear or quadratic problem can easily be transformed into a linear one, but it ...

ArXiv2020

Low-Rank Updates And A Divide-And-Conquer Method For Linear Matrix Equations

Daniel Kressner, Stefano Massei

Linear matrix equations, such as the Sylvester and Lyapunov equations, play an important role in various applications, including the stability analysis and dimensionality reduction of linear dynamical control systems and the solution of partial differentia ...

SIAM PUBLICATIONS2019

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

MATHICSE Technical Report : Fast solvers for 2D fractional differential equations using rank structured matrices

Marco Mazza, Stefano Massei

We consider the discretization of time-space diffusion equations with fractional derivatives in space and either 1D or 2D spatial domains. The use of implicit Euler scheme in time and finite differences or finite elements in space, leads to a sequence of d ...

MATHICSE2018

Unlabeled Sensing with Random Linear Measurements

Martin Vetterli, Jayakrishnan Unnikrishnan, Saeid Haghighatshoar

We study the problem of solving a linear sensing system when the observations are unlabeled. Specifically we seek a solution to a linear system of equations y = Ax when the order of the observations in the vector y is unknown. Focusing on the setting in wh ...

Institute of Electrical and Electronics Engineers2018

MATHICSE Technical Report : Low-rank updates and divide-andconquer methods for quadratic matrix equations

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On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

Iterative refinement of Schur decompositions

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

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

New Results in Integer and Lattice Programming

Matrix recovery from bilinear and quadratic measurements

Low-Rank Updates And A Divide-And-Conquer Method For Linear Matrix Equations

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

MATHICSE Technical Report : Fast solvers for 2D fractional differential equations using rank structured matrices

Unlabeled Sensing with Random Linear Measurements

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

Iterative refinement of Schur decompositions

Matrix recovery from bilinear and quadratic measurements

New Results in Integer and Lattice Programming

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

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

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

Low-Rank Updates And A Divide-And-Conquer Method For Linear Matrix Equations

Unlabeled Sensing with Random Linear Measurements

MATHICSE Technical Report : Fast solvers for 2D fractional differential equations using rank structured matrices