Related papers: The Generalized Matrix Norm Problem

A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…

The generalized operator-based Prony method is an important tool for describing signals which can be written as finite linear combinations of eigenfunctions of certain linear operators. On the other hand, Bernoulli's algorithm and its…

In many fundamental combinatorial optimization problems, a feasible solution induces some real cost vectors as an intermediate result, and the optimization objective is a certain function of the vectors. For example, in the problem of…

In this paper we present a deterministic polynomial time algorithm for testing if a symbolic matrix in non-commuting variables over $\mathbb{Q}$ is invertible or not. The analogous question for commuting variables is the celebrated…

We consider a class of pattern matching problems where a normalising transformation is applied at every alignment. Normalised pattern matching plays a key role in fields as diverse as image processing and musical information processing…

We present a new algorithm for solving a polynomial program P based on the recent "joint + marginal" approach of the first author for, parametric optimization. The idea is to first consider the variable x1 as a parameter and solve the…

The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In…

We study quantum algorithms for approximating Lasserre's hierarchy values for polynomial optimization. Let $f,g_1,\ldots,g_m$ be real polynomials in $n$ variables and $f^\star$ the infimum of $f$ over the semialgebraic set $S(g)=\{x:…

Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and…

We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct:…

There are various inverse problems -- including reconstruction problems arising in medical imaging -- where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask…

This paper considers the problem of scheduling jobs on single and parallel machines where all the jobs possess different processing times but a common due date. There is a penalty involved with each job if it is processed earlier or later…

The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…

We establish a new description of the Schur-Agler norm of a holomorphic function on the polydisc as the solution of a convex optimization problem. Consequences of this description are explored both from a theoretical and from a practical…

Some properties and relations satisfied by the polynomial solutions of the bispectral problem are studied. Given a differential operator, under certain restrictions its polynomial eigenfunctions are explicitly obtained, as well as the…

After reconsidering the theorem of continuity of the roots of a polynomial in terms of its coefficients in the deformation framework, we study the stability of the greater common divisor of two polynomials compared to perturbations on their…

In this note, we introduce generalized powers of linear operators. More precisely, operators are not raised to numbers but to other operators. We discuss several properties as regards this notion.

We consider the problem of computing the family of operator norms recently introduced in arXiv:0909.3907. We develop a family of semidefinite programs that can be used to exactly compute them in small dimensions and bound them in general.…

The nonlinear inverse problem of exponential data fitting is separable since the fitting function is a linear combination of parameterized exponential functions, thus allowing to solve for the linear coefficients separately from the…

We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Algebra 1(2), 1973, pp. 163-171]. Our algorithms are based on…