Publications related to Low-rank methods for parameter-dependent eigenvalue problems and matrix equations

On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems

Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems and eigenvalue p ...

Elsevier Science Inc2016

Projection Methods For Large-Scale T-Sylvester Equations

Daniel Kressner

The matrix Sylvester equation for congruence, or T-Sylvester equation, has recently attracted considerable attention as a consequence of its close relation to palindromic eigenvalue problems. The theory concerning T-Sylvester equations is rather well under ...

Amer Mathematical Soc2016

Compressive PCA for Low-Rank Matrices on Graphs

Pierre Vandergheynst, Gilles Puy, Nathanaël Perraudin, Nauman Shahid

We introduce a novel framework for an approxi- mate recovery of data matrices which are low-rank on graphs, from sampled measurements. The rows and columns of such matrices belong to the span of the first few eigenvectors of the graphs constructed between ...

Ieee-Inst Electrical Electronics Engineers Inc2016

Truncated low-rank methods for solving general linear matrix equations

Daniel Kressner, Petar Sirkovic

This work is concerned with the numerical solution of large-scale linear matrix equations A1XB1T++AKXBKT=C. The most straightforward approach computes XRmxn from the solution of an mn x mn linear system, typically limiting the feasible values of m,n to a f ...

Wiley-Blackwell2015

MATHICSE Technical Report : Subspace acceleration for large-scale parameter-dependent Hermitian eigenproblems

Daniel Kressner, Petar Sirkovic

This work is concerned with approximating the smallest eigenvalue of a parameter-dependent Hermitian matrix A(μ) for many parameter values μ ∈ RP. The design of reliable and efficient algorithms for addressing this task is of importance in a variety of app ...

MATHICSE2015

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Afsaneh Asaei, Mohammadjavad Taghizadeh, Saeid Haghighatshoar

In this paper, we prove a new identity for the least-square solution of an over-determined set of linear equation

Ax=b

, where

A

is an

m\times n

full-rank matrix,

b

is a column-vector of dimension

m

, and

m

(the number of equations) is larger tha ...

2015

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Afsaneh Asaei, Mohammadjavad Taghizadeh, Saeid Haghighatshoar

In this paper, we prove a new identity for the least-square solution of an over-determined set of linear equation

Ax=b

, where

A

is an

m\times n

full-rank matrix,

b

is a column-vector of dimension

m

, and

m

(the number of equations) is larger tha ...

Idiap2015

MATHICSE Technical Report: Reduced basis methods: from low-rank matrices to low-rank tensor

Daniel Kressner, Jonas Ballani

We propose a novel combination of the reduced basis method with low-rank tensor techniques for the efficient solution of parameter-dependent linear systems in the case of several parameters. This combination, called rb Tensor, consists of three ingredients ...

MATHICSE2015

Low rank differential equations for Hamiltonian matrix nearness problems

Daniel Kressner

For a Hamiltonian matrix with purely imaginary eigenvalues, we aim to determine the nearest Hamiltonian matrix such that some or all eigenvalues leave the imaginary axis. Conversely, for a Hamiltonian matrix with all eigenvalues lying off the imaginary axi ...

Springer Heidelberg2015

Low-Rank Tensor Methods With Subspace Correction For Symmetric Eigenvalue Problems

Daniel Kressner, André Uschmajew, Michael Maximilian Steinlechner

We consider the solution of large-scale symmetric eigenvalue problems for which it is known that the eigenvectors admit a low-rank tensor approximation. Such problems arise, for example, from the discretization of high-dimensional elliptic PDE eigenvalue p ...

Siam Publications2014

Low-rank methods for parameter-dependent eigenvalue problems and matrix equations

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On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems

Projection Methods For Large-Scale T-Sylvester Equations

Compressive PCA for Low-Rank Matrices on Graphs

Truncated low-rank methods for solving general linear matrix equations

MATHICSE Technical Report : Subspace acceleration for large-scale parameter-dependent Hermitian eigenproblems

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

MATHICSE Technical Report: Reduced basis methods: from low-rank matrices to low-rank tensor

Low rank differential equations for Hamiltonian matrix nearness problems

Low-Rank Tensor Methods With Subspace Correction For Symmetric Eigenvalue Problems

MATHICSE Technical Report : Subspace acceleration for large-scale parameter-dependent Hermitian eigenproblems

Projection Methods For Large-Scale T-Sylvester Equations

On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems

Compressive PCA for Low-Rank Matrices on Graphs

Truncated low-rank methods for solving general linear matrix equations

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

MATHICSE Technical Report: Reduced basis methods: from low-rank matrices to low-rank tensor

Low-Rank Tensor Methods With Subspace Correction For Symmetric Eigenvalue Problems

Low rank differential equations for Hamiltonian matrix nearness problems