Publications related to Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials

Parity-Time Symmetric Nonlocal Metamaterials for Focusing and Image Processing

Parity-Time (PT) symmetry refers to the invariance of a physical system upon reflection of space and time. An intriguing property of PT-symmetric quantum systems is the fact that they can have entirely real eigenvalue spectra, despite being non-Hermitian. ...

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 ...

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

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

Fabio Nobile, Giovanni Migliorati

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate func- tions based on random sampling according to a given probability measure. Recent work has shown th ...

MATHICSE2014

Inner approximations of the region of attraction for polynomial dynamical systems

Colin Neil Jones, Milan Korda

In a previous work we developed a convex infinite dimensional linear programming (LP) approach to approximating the region of attraction (ROA) of polynomial dynamical systems subject to compact basic semialgebraic state constraints. Finite dimensional rela ...

2013

Hermitian Forms over Algebras with Involution and Hermitian Categories

Daniel Arnold Moldovan

This thesis is concerned with the algebraic theory of hermitian forms. It is organized in two parts. The first, consisting of the first two chapters, deals with some descent properties of unimodular hermitian forms over central simple algebras with involut ...

EPFL2012

Optimal Linear Fusion for Distributed Detection Via Semidefinite Programming

Ali H. Sayed

Consider the problem of signal detection via multiple distributed noisy sensors. We study a linear decision fusion rule of [Z. Quan, S. Cui, and A. H. Sayed, ¿Optimal Linear Cooperation for Spectrum Sensing in Cognitive Radio Networks,¿ IEEE J. Sel. Topics ...

IEEE2010

Block variants of Hammarling's method for solving Lyapunov equations

Daniel Kressner

This article is concerned with the efficient numerical solution of the Lyapunov equation A(T) X + XA = -C with a stable matrix A and a symmetric positive semidefinite matrix C of possibly small rank. We discuss the efficient implementation of Hammarling's ...

Association for Computing Machinery2008

A polynomial case of inconstrained zero-one queadratic optimization

Thomas Liebling, Kim Alexandre Allemand

Unconstrained zero-one quadratic maximization problems can be solved in polynomial time when the symmetric matrix describing the objective function is positive semidefinite of fixed rank with known spectral decomposition. ...

2001

Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials

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Parity-Time Symmetric Nonlocal Metamaterials for Focusing and Image Processing

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

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

Inner approximations of the region of attraction for polynomial dynamical systems

Hermitian Forms over Algebras with Involution and Hermitian Categories

Optimal Linear Fusion for Distributed Detection Via Semidefinite Programming

Block variants of Hammarling's method for solving Lyapunov equations

A polynomial case of inconstrained zero-one queadratic optimization

Parity-Time Symmetric Nonlocal Metamaterials for Focusing and Image Processing

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

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

Hermitian Forms over Algebras with Involution and Hermitian Categories

Block variants of Hammarling's method for solving Lyapunov equations

A polynomial case of inconstrained zero-one queadratic optimization

Approximate Matrix Multiplication with Application to Linear Embeddings

Inner approximations of the region of attraction for polynomial dynamical systems

Optimal Linear Fusion for Distributed Detection Via Semidefinite Programming