Related papers: Sparse Tensors and Subdivision Methods for Finding…
The works presented in this habilitation concern the algorithmics of polynomials. This is a central topic in computer algebra, with numerous applications both within and outside the field - cryptography, error-correcting codes, etc. For…
In this paper, we give new sparse interpolation algorithms for black box polynomial f whose coefficients are from a finite set. In the univariate case, we recover f from one evaluation of f(a) for a sufficiently large number a. In the…
We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block Gaussian elimination and additionally compress the fill-in.…
We propose a fast greedy algorithm to compute sparse representations of signals from continuous dictionaries that are factorizable, i.e., with atoms that can be separated as a product of sub-atoms. Existing algorithms strongly reduce the…
Finding sparse solutions of underdetermined systems of linear equations is a fundamental problem in signal processing and statistics which has become a subject of interest in recent years. In general, these systems have infinitely many…
This work investigates an efficient solution to two fundamental problems in topology optimization of frame structures. The first one involves minimizing structural compliance under linear-elastic equilibrium and weight constraint, while the…
We show how one can phrase the cut improvement problem for graphs as a sparse recovery problem, whence one can use algorithms originally developed for use in compressive sensing (such as SubspacePursuit or CoSaMP) to solve it. We show that…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
Exact recovery of a sparse solution for an underdetermined system of linear equations implies full search among all possible subsets of the dictionary, which is computationally intractable, while l1 minimization will do the job when a…
We present a novel feature selection technique, Sparse Linear Centroid-Encoder (SLCE). The algorithm uses a linear transformation to reconstruct a point as its class centroid and, at the same time, uses the $\ell_1$-norm penalty to filter…
This paper proposes a method for solving multivariate regression and classification problems using piecewise linear predictors over a polyhedral partition of the feature space. The resulting algorithm that we call PARC (Piecewise Affine…
In the present work, we study how to develop an efficient solver for the fast resolution of large and sparse linear systems that occur while discretizing elliptic partial differential equations using isogeometric analysis. Our new approach…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
Spectral Clustering is one of the most traditional methods to solve segmentation problems. Based on Normalized Cuts, it aims at partitioning an image using an objective function defined by a graph. Despite their mathematical attractiveness,…
This work investigates the use of sparse polynomial interpolation as a model order reduction method for the incompressible Navier-Stokes equations. Numerical results are presented underscoring the validity of sparse polynomial…
Sparse matrix-vector multiplication (SpMV) is a central building block for scientific software and graph applications. Recently, heterogeneous processors composed of different types of cores attracted much attention because of their…
By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study,…
We consider the problem of solving mixed random linear equations with $k$ components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels…
Efficient handling of sparse data is a key challenge in Computer Science. Binary convolutions, such as polynomial multiplication or the Walsh Transform are a useful tool in many applications and are efficiently solved. In the last decade,…
We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…