Publications related to Truncated low-rank methods for solving general linear matrix equations

MATHICSE Technical Report : Preconditioned low-rank Riemannian optimization for linear systems with tensor product structure

Daniel Kressner, Michael Maximilian Steinlechner

The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially with the number ...

MATHICSE2015

MATHICSE Technical Report : Isogeometric analysis of high order partial differential equations on surfaces

Alfio Quarteroni, Luca Dede', Andrea Bartezzaghi

We consider the numerical approximation of high order Partial Differential Equations (PDEs) defined on surfaces in the three dimensional space, with particular emphasis on closed surfaces. We consider computational domains that can be represented by B-spli ...

MATHICSE2015

Isogeometric Analysis for second order Partial Differential Equations on surfaces

Alfio Quarteroni, Luca Dede'

We consider the numerical solution of second order Partial Differential Equations (PDEs) on lower dimensional manifolds, specifically on surfaces in three dimensional spaces. For the spatial approximation, we consider Isogeometric Analysis which facilitate ...

Elsevier2015

Isogeometric Analysis of high order Partial Differential Equations on surfaces

Alfio Quarteroni, Luca Dede', Andrea Bartezzaghi

We consider the numerical approximation of high order Partial Differential Equations (PDEs) defined on surfaces in the three dimensional space, with particular emphasis on closed surfaces. We consider computational domains that can be represented by B-spli ...

Elsevier2015

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

Matrix-product-operator approach to the nonequilibrium steady state of driven-dissipative quantum arrays

Vincenzo Savona, Hugo Pierre Alexandre Flayac, Eduardo Carlo Mascarenhas Moraes

We develop a numerical procedure to efficiently model the nonequilibrium steady state of one-dimensional arrays of open quantum systems based on a matrix-product operator ansatz for the density matrix. The procedure searches for the null eigenvalue of the ...

American Physical Society2015

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

Bivariate Matrix Functions

Daniel Kressner

A definition of bivariate matrix functions is introduced and some theoretical as well as algorithmic aspects are analyzed. It is shown that our framework naturally extends the usual notion of (univariate) matrix functions and allows to unify existing resul ...

Element2014

LINVIEW: Incremental View Maintenance for Complex Analytical Queries

Christoph Koch, Milos Nikolic, Mohamed Elsayed Mohamed Ahmed El Seidy

Many analytics tasks and machine learning problems can be naturally expressed by iterative linear algebra programs. In this paper, we study the incremental view maintenance problem for such complex analytical queries. We develop a framework, called LINVIEW ...

2014

Truncated low-rank methods for solving general linear matrix equations

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MATHICSE Technical Report : Preconditioned low-rank Riemannian optimization for linear systems with tensor product structure

MATHICSE Technical Report : Isogeometric analysis of high order partial differential equations on surfaces

Isogeometric Analysis for second order Partial Differential Equations on surfaces

Isogeometric Analysis of high order Partial Differential Equations on surfaces

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

Matrix-product-operator approach to the nonequilibrium steady state of driven-dissipative quantum arrays

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

Bivariate Matrix Functions

LINVIEW: Incremental View Maintenance for Complex Analytical Queries

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

Isogeometric Analysis of high order Partial Differential Equations on surfaces

MATHICSE Technical Report : Isogeometric analysis of high order partial differential equations on surfaces

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

Isogeometric Analysis for second order Partial Differential Equations on surfaces

MATHICSE Technical Report : Preconditioned low-rank Riemannian optimization for linear systems with tensor product structure

Bivariate Matrix Functions

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

LINVIEW: Incremental View Maintenance for Complex Analytical Queries

Matrix-product-operator approach to the nonequilibrium steady state of driven-dissipative quantum arrays