Publications related to Preconditioning techniques for generalized Sylvester matrix equations

Mega Event Reinforced Industrial Heritage Transformation: A typological matrix between narratives and practices

Mega-events have been considered as a strategy to boost urban development, which shifts targets from expansion outside of the original city fabric to reuse of heritage. The bidirectional dynamic between mega-events and heritage has been emphasized, as the ...

2022

A Determinantal Identity for the Permanent of a Rank 2 Matrix

Adam Wade Marcus

We prove an identity relating the permanent of a rank 2 matrix and the determinants of its Hadamard powers. When viewed in the right way, the resulting formula looks strikingly similar to an identity of Carlitz and Levine, suggesting the possibility that t ...

TAYLOR & FRANCIS INC2022

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

Efficient Learning of a Linear Dynamical System with Stability Guarantees

Daniel Kuhn, Wouter Jongeneel, Tobias Sutter

We propose a principled method for projecting an arbitrary square matrix to the non- convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an information-theoretic sense and ...

2021

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

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

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

Daniel Kressner, Stefano Massei

Matrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile tool to develop fast algorithms for addressing large-scale problems. While existing software packages for such matrices often focus on linear systems, t ...

SIAM PUBLICATIONS2020

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

hm-toolbox: Matlab software for HODLR and HSS matrices

Daniel Kressner, Stefano Massei

Matrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile tool to develop fast algorithms for addressing large-scale problems. While existing software packages for such matrices often focus on linear systems, t ...

2019

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

Stefano Massei

A Quasi Toeplitz (QT) matrix is a semi-infinite matrix of the kind

A = T(a) + E

where

T(a) = (aj-i)_{i,j\in \mathbb{Z}_{+}}

,

E = (e_{i,j})_{i,j\in\mathbb{Z}_{+}}

is compact and the norms

\| a\|_{\mathcal{W}} =\sum_{i\in\mathbb{Z}} |a|_j

and $|E|_{ ...

MATHICSE2018

Preconditioning techniques for generalized Sylvester matrix equations

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Mega Event Reinforced Industrial Heritage Transformation: A typological matrix between narratives and practices

A Determinantal Identity for the Permanent of a Rank 2 Matrix

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

Efficient Learning of a Linear Dynamical System with Stability Guarantees

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

Recursive blocked algorithms for linear systems with Kronecker product structure

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

hm-toolbox: Matlab software for HODLR and HSS matrices

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

A Determinantal Identity for the Permanent of a Rank 2 Matrix

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

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

Mega Event Reinforced Industrial Heritage Transformation: A typological matrix between narratives and practices

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

Recursive blocked algorithms for linear systems with Kronecker product structure

hm-toolbox: Matlab software for HODLR and HSS matrices

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

Efficient Learning of a Linear Dynamical System with Stability Guarantees