Publications related to hm-toolbox: Matlab software for HODLR and HSS matrices

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

On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Daniel Kressner, Stefano Massei, Alice Cortinovis

The problem of finding a k x k submatrix of maximum volume of a matrix A is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of A. We show that such a submatrix can a ...

ELSEVIER SCIENCE INC2020

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

Global eigenvalue distribution of matrices defined by the skew-shift

Marius Christopher Lemm

We consider large Hermitian matrices whose entries are defined by evaluating the exponential function along orbits of the skew-shift

\binom{j}{2} \omega+jy+x \mod 1

for irrational

\omega

. We prove that the eigenvalue distribution of these matrices conv ...

2019

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

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Daniel Kressner, Stefano Massei, Alice Cortinovis

The problem of finding a

k\times k

submatrix of maximum volume of a matrix A is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of A. We show that such a submatrix ...

MATHICSE2019

Multi-panel, on-single-chip Memristive Biosensing

Giovanni De Micheli, Sandro Carrara, Danilo Demarchi, Ioulia Tzouvadaki, Abuduwaili Tuoheti

Memristive biosensors have demonstrated excellent capabilities for ultrasensitive bio-detection. In the present work, memristive biosensing chips are designed, fabricated and implemented in a for the first time presented multi-panel on-chip detection for d ...

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

Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization

Sebastian Urban Stich

We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive definite matrices i ...

2018

hm-toolbox: Matlab software for HODLR and HSS matrices

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

Recursive blocked algorithms for linear systems with Kronecker product structure

On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

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

Global eigenvalue distribution of matrices defined by the skew-shift

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Multi-panel, on-single-chip Memristive Biosensing

Fast hierarchical solvers for symmetric eigenvalue problems

Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization

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

Recursive blocked algorithms for linear systems with Kronecker product structure

On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Global eigenvalue distribution of matrices defined by the skew-shift

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Multi-panel, on-single-chip Memristive Biosensing

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Fast hierarchical solvers for symmetric eigenvalue problems

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

Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization