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We show that a generalised sparse grid combination technique which combines multi-variate extrapolation of finite difference solutions with the standard combination formula lifts a second order accurate scheme on regular meshes to a fourth…
The multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared to…
We study how the complexity of modular circuits computing AND depends on the depth of the circuits and the prime factorization of the modulus they use. In particular our construction of subexponential circuits of depth 2 for AND helps us to…
We consider the problem of interpolating an unknown multivariate polynomial with coefficients taken from a finite field or as numerical approximations of complex numbers. Building on the recent work of Garg and Schost, we improve on the…
This paper proposes an efficient probabilistic method that computes combinatorial gradient fields for two dimensional image data. In contrast to existing algorithms, this approach yields a geometric Morse-Smale complex that converges almost…
We give a high precision polynomial-time approximation scheme for the supremum of any honest n-variate (n+2)-nomial with a constant term, allowing real exponents as well as real coefficients. Our complexity bounds count field operations and…
In this paper, a sparse-based method for the estimation of the parameters of multidimensional ($R$-D) modal (harmonic or damped) complex signals in noise is presented. The problem is formulated as $R$ simultaneous sparse approximations of…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
We present an algorithm to perform a simultaneous modular reduction of several residues. This algorithm is applied fast modular polynomial multiplication. The idea is to convert the $X$-adic representation of modular polynomials, with $X$…
In this work, we deal with the problem of computing a comprehensive front of efficient solutions in multi-objective portfolio optimization problems in presence of sparsity constraints. We start the discussion pointing out some weaknesses of…
We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in…
Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the…
Based on the Bezout approach we propose a simple algorithm to determine the {\tt gcd} of two polynomials which doesn't need division, like the Euclidean algorithm, or determinant calculations, like the Sylvester matrix algorithm. The…
We study the problem of minimizing a multivariate polynomial function over the unit hypercube. By representing the polynomial through a hypergraph and exploiting its sparsity structure, we establish a new sufficient condition under which…
Gaussian processes (GPs) are typically criticised for their unfavourable scaling in both computational and memory requirements. For large datasets, sparse GPs reduce these demands by conditioning on a small set of inducing variables…
We introduce a soft computing approach for automatically selecting and combining indices from remote sensing multispectral images that can be used for classification tasks. The proposed approach is based on a Genetic-Programming (GP)…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
In recent years many sparse linear discriminant analysis methods have been proposed for high-dimensional classification and variable selection. However, most of these proposals focus on binary classification and they are not directly…
Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly…
Counting distinct permutations with replacement, especially when involving multiple subwords, is a longstanding challenge in combinatorial analysis, with critical applications in cryptography, bioinformatics, and statistical modeling. This…