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We study the Electrical Impedance Tomography Bayesian inverse problem for recovering the conductivity given noisy measurements of the voltage on some boundary surface electrodes. The uncertain conductivity depends linearly on a countable…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
Parametric model order reduction (pMOR) is a powerful tool for accelerating finite element (FE) simulations while maintaining parametric dependencies. For geometric parameters, pMOR by matrix interpolation is a well-suited approach because…
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…
This article studies separating invariants for the ring of multisymmetric polynomials in $m$ sets of $n$ variables over an arbitrary field $\mathbb{K}$. We prove that in order to obtain separating sets it is enough to consider polynomials…
The aim of this work is to show how symbolic computation can be used to perform multivariate Lagrange, Hermite and Birkhoff interpolation and help us to build more realistic interpolating functions. After a theoretical introduction in which…
The objective of the matrix selection problem is to select a submatrix $A_{S}\in \mathbb{R}^{n\times k}$ from $A\in \mathbb{R}^{n\times m}$ such that its minimum singular value is maximized. In this paper, we employ the interlacing…
List decoding of Hermitian codes is reformulated to allow an efficient and simple algorithm for the interpolation step. The algorithm is developed using the theory of Groebner bases of modules. The computational complexity of the algorithm…
A multilevel kernel-based interpolation method, suitable for moderately high-dimensional function interpolation problems, is proposed. The method, termed multilevel sparse kernel-based interpolation (MLSKI, for short), uses both level-wise…
Many high dimensional integrals can be reduced to the problem of finding the relative measures of two sets. Often one set will be exponentially larger than the other, making it difficult to compare the sizes. A standard method of dealing…
The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their…
Nonlinear interpolants have been shown useful for the verification of programs and hybrid systems in contexts of theorem proving, model checking, abstract interpretation, etc. The underlying synthesis problem, however, is challenging and…
Based on the computation of a superset of the implicit support, implicitization of a parametrically given hyper-surface is reduced to computing the nullspace of a numeric matrix. Our approach exploits the sparseness of the given parametric…
In this paper, we provide a local method to find compositional inverses of all PPs, some new PPs and their compositional inverses are given.
The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical…
In this paper we present a minimal list decoding algorithm for Reed-Solomon (RS) codes. Minimal list decoding for a code $C$ refers to list decoding with radius $L$, where $L$ is the minimum of the distances between the received word…
We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…
In this paper we present a new multilevel quasi-interpolation algorithm for smooth periodic functions using scaled Gaussians as basis functions. Recent research in this area has focussed upon implementations using basis function with finite…
This article proposes a bivariate polynomial problem for finite-order real matrices that endows a \textit{`sufficient condition'} for a map from the standard vector spaces of finite-order real matrices to the same dimensional bivariate…
Many computer vision applications require robust estimation of the underlying geometry, in terms of camera motion and 3D structure of the scene. These robust methods often rely on running minimal solvers in a RANSAC framework. In this paper…