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

A hierarchical preconditioner for wave problems in quasilinear complexity

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

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

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

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

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

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

Daniel Kressner, Stefano Massei

In this work, we consider two types of large-scale quadratic matrix equations: Continuous-time algebraic Riccati equations, which play a central role in optimal and robust control, and unilateral quadratic matrix equations, which arise from stochastic proc ...

MATHICSE2019

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

Fast hierarchical solvers for symmetric eigenvalue problems

Ana Susnjara

In this thesis we address the computation of a spectral decomposition for symmetric banded matrices. In light of dealing with large-scale matrices, where classical dense linear algebra routines are not applicable, it is essential to design alternative tech ...

EPFL2018

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

A reduced order accelerator for time-dependent segregated neutronic solvers

Andreas Pautz, Carlo Fiorina, Alessandro Scolaro, Stefan Radman

The deterministic solution of the neutron transport problem entails the coupled solution of several partial differential equations, one for each energy group, direction and/or spherical harmonic. Several techniques have been devised for accelerating the so ...

PERGAMON-ELSEVIER SCIENCE LTD2018

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

Graph Chatbot

Chat with Graph Search

A hierarchical preconditioner for wave problems in quasilinear complexity

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

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

hm-toolbox: Matlab software for HODLR and HSS matrices

Backpropagation-Friendly Eigendecomposition

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

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Fast hierarchical solvers for symmetric eigenvalue problems

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

A reduced order accelerator for time-dependent segregated neutronic solvers

A hierarchical preconditioner for wave problems in quasilinear complexity

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

Fast hierarchical solvers for symmetric eigenvalue problems

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

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

hm-toolbox: Matlab software for HODLR and HSS matrices

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

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

A reduced order accelerator for time-dependent segregated neutronic solvers

Backpropagation-Friendly Eigendecomposition