Publications related to A Fast Stable Solver for Nonsymmetric Toeplitz and Quasi-Toeplitz Systems of Linear Equations

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

A Quasi Toeplitz (QT) matrix is a semi-infinite matrix of the kind

A = T(a) + E

where

T(a) = (aj-i)_{i,j\in \mathbb{Z}_{+}}

,

E = (e_{i,j})_{i,j\in\mathbb{Z}_{+}}

is compact and the norms

\| a\|_{\mathcal{W}} =\sum_{i\in\mathbb{Z}} |a|_j

and $|E|_{ ...

MATHICSE2018

MATHICSE Technical Report : Solving rank structured Sylvester and Lyapunov equations

Stefano Massei

We consider the problem of efficiently solving Sylvester and Lyapunov equations of medium and large scale, in case of rank-structured data, i.e., when the coefficient matrices and the right-hand side have low-rank off- diagonal blocks. This comprises probl ...

MATHICSE2017

ALS Scheme using Extent-based Constraints for the Analysis of Chemical Reaction Systems

Dominique Bonvin, Julien Léo Billeter, Michael Amrhein

Multivariate curve resolution via alternating least squares (ALS) is used to resolve the concentration profiles C and the pure component spectra E of S species from the multivariate absorbance data A, assuming the bilinear model ...

2016

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

Petar Sirkovic

The focus of this thesis is on developing efficient algorithms for two important problems arising in model reduction, estimation of the smallest eigenvalue for a parameter-dependent Hermitian matrix and solving large-scale linear matrix equations, by extra ...

EPFL2016

A block algorithm for computing antitriangular factorizations of symmetric matrices

Daniel Kressner, Zvonimir Bujanovic

Any symmetric matrix can be reduced to antitriangular form in finitely many steps by orthogonal similarity transformations. This form reveals the inertia of the matrix and has found applications in, e.g., model predictive control and constraint preconditio ...

Springer2016

Converse Bounds for Noisy Group Testing with Arbitrary Measurement Matrices

Volkan Cevher, Jonathan Mark Scarlett

We consider the group testing problem, in which one seeks to identify a subset of defective items within a larger set of items based on a number of noisy tests. While matching achievability and converse bounds are known in several cases of interest for i.i ...

Ieee2016

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

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

Approximate Matrix Multiplication with Application to Linear Embeddings

Michail Vlachos, Anastasios Kyrillidis

In this paper, we study the problem of approximately computing the product of two real matrices. In particular, we analyze a dimensionality-reduction-based approximation algorithm due to Sarlos [1], introducing the notion of nuclear rank as the ratio of th ...

Ieee2014

A Fast Stable Solver for Nonsymmetric Toeplitz and Quasi-Toeplitz Systems of Linear Equations

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MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

MATHICSE Technical Report : Solving rank structured Sylvester and Lyapunov equations

ALS Scheme using Extent-based Constraints for the Analysis of Chemical Reaction Systems

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

A block algorithm for computing antitriangular factorizations of symmetric matrices

Converse Bounds for Noisy Group Testing with Arbitrary Measurement Matrices

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

Approximate Matrix Multiplication with Application to Linear Embeddings

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

A block algorithm for computing antitriangular factorizations of symmetric matrices

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

Approximate Matrix Multiplication with Application to Linear Embeddings

Truncated low-rank methods for solving general linear matrix equations

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

MATHICSE Technical Report : Solving rank structured Sylvester and Lyapunov equations

Converse Bounds for Noisy Group Testing with Arbitrary Measurement Matrices

ALS Scheme using Extent-based Constraints for the Analysis of Chemical Reaction Systems

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