Publications related to MATHICSE Technical Report : A fast spectral divide-and-conquer method for banded matrices

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

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

Siam Publications2024

A 16-bit Floating-Point Near-SRAM Architecture for Low-power Sparse Matrix-Vector Multiplication

David Atienza Alonso, Giovanni Ansaloni, Grégoire Axel Eggermann, Marco Antonio Rios

State-of-the-art Artificial Intelligence (AI) algorithms, such as graph neural networks and recommendation systems, require floating-point computation of very large matrix multiplications over sparse data. Their execution in resource-constrained scenarios, ...

2023

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

TimeEvolver: A program for time evolution with improved error bound

Sebastian Zell

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

ELSEVIER2022

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

A fast spectral divide-and-conquer method for banded matrices

Daniel Kressner, Ana Susnjara

Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3):A1325-A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix with small bandwidth, w ...

WILEY2021

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

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

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

A Householder-Based Algorithm For Hessenberg-Triangular Reduction

Daniel Kressner, Zvonimir Bujanovic

The QZ algorithm for computing eigenvalues and eigenvectors of a matrix pencil A - lambda B requires that the matrices first be reduced to Hessenberg-triangular (HT) form. The current method of choice for HT reduction relies entirely on Givens rotations re ...

SIAM PUBLICATIONS2018

MATHICSE Technical Report : A fast spectral divide-and-conquer method for banded matrices

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

A 16-bit Floating-Point Near-SRAM Architecture for Low-power Sparse Matrix-Vector Multiplication

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

TimeEvolver: A program for time evolution with improved error bound

Iterative refinement of Schur decompositions

A fast spectral divide-and-conquer method for banded matrices

New Results in Integer and Lattice Programming

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

Fast hierarchical solvers for symmetric eigenvalue problems

A Householder-Based Algorithm For Hessenberg-Triangular Reduction

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

A 16-bit Floating-Point Near-SRAM Architecture for Low-power Sparse Matrix-Vector Multiplication

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

TimeEvolver: A program for time evolution with improved error bound

New Results in Integer and Lattice Programming

Fast hierarchical solvers for symmetric eigenvalue problems

A Householder-Based Algorithm For Hessenberg-Triangular Reduction

Iterative refinement of Schur decompositions

A fast spectral divide-and-conquer method for banded matrices

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