Related papers: A quotient framework for single-input pole placeme…
This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs…
In this paper we analyze and solve eigenvalue programs, which consist of the task of minimizing a function subject to constraints on the "eigenvalues" of the decision variable. Here, by making use of the FTvN systems framework introduced by…
We introduce a unified method for study of 2-dimensional invariant subspaces of matrices and their corresponding super-eigenvalues. As a novel application to non-commutative algebra, we present a connection between the eigenvalues of…
Given a random quantum state of multiple distinguishable or indistinguishable particles, we provide an effective method, rooted in symplectic geometry, to compute the joint probability distribution of the eigenvalues of its one-body reduced…
The computation of the sparse principal component of a matrix is equivalent to the identification of its principal submatrix with the largest maximum eigenvalue. Finding this optimal submatrix is what renders the problem…
We describe new algorithms to compute Whitney stratifications of real algebraic varieties. Using either conormal or polar techniques, these algorithms stratify a complexification of a given real variety. We then show that the resulting…
The problem of estimating sparse eigenvectors of a symmetric matrix attracts a lot of attention in many applications, especially those with high dimensional data set. While classical eigenvectors can be obtained as the solution of a…
The paper studies a general inverse eigenvalue problem which contains as special cases many well studied pole placement and matrix extension problems. It is shown that the studied problem corresponds on the geometric side to a central…
We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of…
The problem of approximating a dense matrix by a product of sparse factors is a fundamental problem for many signal processing and machine learning tasks. It can be decomposed into two subproblems: finding the position of the non-zero…
This paper discusses the spectral collocation method for numerically solving nonlocal problems: one dimensional space fractional advection-diffusion equation; and two dimensional linear/nonlinear space fractional advection-diffusion…
When applying eigenvalue decomposition on the quadratic term matrix in a type of linear equally constrained quadratic programming (EQP), there exists a linear mapping to project optimal solutions between the new EQP formulation where $Q$ is…
We develop a new algorithm for factoring a bivariate polynomial $F\in \mathbb{K}[x,y]$ which takes fully advantage of the geometry of the Newton polygon of $F$. Under a non degeneracy hypothesis, the complexity is…
The scheme of divided differences is widely used in many approximation and interpolation problems. Computing the Newton coefficients of the interpolating polynomial is the first step of the Bj\"{o}rck and Pereyra algorithm for solving…
We study linear difference equations with variable coefficients in a ring using a new nonlinear method. In a ring with identity, if the homogeneous part of the linear equation has a solution in the unit group of the ring (i.e., a unitary…
This paper presents a new algorithm to estimate absolute camera pose given an axis of the camera's rotation matrix. Current algorithms solve the problem via algebraic solutions on limited input domains. This paper shows that the problem can…
We present an alternative algorithm to global fitting procedures to construct Parton Distribution Functions (PDFs) parametrizations. The proposed algorithm uses Self-Organizing Maps (SOMs) which at variance with the standard Neural…
In this paper we address the problem of unsupervised localization of objects in single images. Compared to previous state-of-the-art method our method is fully unsupervised in the sense that there is no prior instance level or category…
We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank. When the rank constraint is active,…
We introduce a family of univariate polynomials indexed by integer partitions. At prime powers, they count the number of subspaces in a finite vector space that transform under a regular diagonal matrix in a specified manner. This…