Related papers: Deterministic Interpolation of Sparse Black-box Mu…

We introduce sparse polynomial zonotopes, a new set representation for formal verification of hybrid systems. Sparse polynomial zonotopes can represent non-convex sets and are generalizations of zonotopes, polytopes, and Taylor models.…

Packing and covering semidefinite programs (SDPs) appear in natural relaxations of many combinatorial optimization problems as well as a number of other applications. Recently, several techniques were proposed, that utilize the particular…

We propose a new method based on sparse optimal discriminant clustering (SODC), incorporating a penalty term into the scoring matrix based on convex clustering. With the addition of this penalty term, it is expected to improve the accuracy…

Advanced algorithms for large-scale electronic structure calculations are mostly based on processing multi-dimensional sparse data. Examples are sparse matrix-matrix multiplications in linear-scaling Kohn-Sham calculations or the efficient…

We introduce determinantal sieving, a new, remarkably powerful tool in the toolbox of algebraic FPT algorithms. Given a polynomial $P(X)$ on a set of variables $X=\{x_1,\ldots,x_n\}$ and a linear matroid $M=(X,\mathcal{I})$ of rank $k$,…

A method is introduced to perform simultaneous sparse dimension reduction on two blocks of variables. Beyond dimension reduction, it also yields an estimator for multivariate regression with the capability to intrinsically deselect…

Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…

Direct factorization methods for the solution of large, sparse linear systems that arise from PDE discretizations are robust, but typically show poor time and memory scalability for large systems. In this paper, we describe an efficient…

To the best of our knowledge this paper is the first attempt to introduce and study polynomial interpolation of the polynomial data given on arbitrary varieties. In the first part of the paper we present results on the solvability of such…

Binary matrix factorisation is an essential tool for identifying discrete patterns in binary data. In this paper we consider the rank-k binary matrix factorisation problem (k-BMF) under Boolean arithmetic: we are given an n x m binary…

In this paper, we present a new framework for the recent multidimensional extrapolation methods: Tensor Global Minimal Polynomial (TG-MPE) and Tensor Global Reduced Rank Extrapolation (TG-RRE) methods. We develop a new approach to the one…

When a black-box optimization objective can only be evaluated with costly or noisy measurements, most standard optimization algorithms are unsuited to find the optimal solution. Specialized algorithms that deal with exactly this situation…

Consider a system of n polynomial equations and r polynomial inequations in n indeterminates of degree bounded by d with coefficients in a polynomial ring of s parameters with rational coefficients of bit-size at most $\sigma$. From the…

This paper focuses on the equidimensional decomposition of affine varieties defined by sparse polynomial systems. For generic systems with fixed supports, we give combinatorial conditions for the existence of positive dimensional components…

Consider a system F of n polynomial equations in n unknowns, over an algebraically closed field of arbitrary characteristic. We present a fast method to find a point in every irreducible component of the zero set Z of F. Our techniques…

We consider the problem of computing univariate polynomial matrices over a field that represent minimal solution bases for a general interpolation problem, some forms of which are the vector M-Pad\'e approximation problem in [Van Barel and…

The sparse generalized eigenvalue problem arises in a number of standard and modern statistical learning models, including sparse principal component analysis, sparse Fisher discriminant analysis, and sparse canonical correlation analysis.…

This work studies the problem of jointly estimating unknown parameters from Kronecker-structured multidimensional signals, which arises in applications like intelligent reflecting surface (IRS)-aided channel estimation. Exploiting the…

Renormalized homotopy continuation on toric varieties is introduced as a tool for solving sparse systems of polynomial equations, or sparse systems of exponential sums. The cost of continuation depends on a renormalized condition length,…

Binary deterministic sensing matrices are highly desirable for sampling sparse signals, as they require only a small number of sum-operations to generate the measurement vector. Furthermore, sparse sensing matrices enable the use of…