Related papers: Relative parametrization of linear multidimensiona…
The geometric and algebraic theory of monomial ideals and multigraded modules is initiated over real-exponent polynomial rings and, more generally, monoid algebras for real polyhedral cones. The main results include the generalization of…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
The aim of this work is to characterize linear maps of inner pro\-duct infinite-dimensional vector spaces where the Moore-Penrose inverse exists. This MP inverse generalizes the well-known Moore-Penrose inverse of a matrix $A\in…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
The efficient inversion of matrix polynomials is a critical challenge in computational mathematics. We design a procedure to determine the inverse of matrices polynomial of multidimensional Laplace matrices. The method is based on…
We propose a method for the construction of preconditioners of parameter-dependent matrices for the solution of large systems of parameter-dependent equations. The proposed method is an interpolation of the matrix inverse based on a…
Dub\'e introduced cone decompositions and their Macaulay constants and used them to obtain an upper bound on the degrees of the generators in a Gr\"obner basis of an ideal. Liang extended the theory to submodules of a free module. In this…
In this article we present a parallel modular algorithm to compute all solutions with multiplicities of a given zero-dimensional polynomial system of equations over the rationals. In fact, we compute a triangular decomposition using…
We extend the Eruguin result exposed in the paper "Construction of the whole set of ordinary differential equations with a given integral curve" published in 1952 and construct a differential system in $\Bbb{R}^N$ which admits a given set…
This paper introduces discrete-holomorphic Perfectly Matched Layers (PMLs) specifically designed for high-order finite difference (FD) discretizations of the scalar wave equation. In contrast to standard PDE-based PMLs, the proposed method…
Reynolds' theory of relational parametricity formalizes parametric polymorphism for System F, thus capturing the idea that polymorphically typed System F programs always map related inputs to related results. This paper shows that Reynolds'…
This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is a new parameterization of the optimality condition which allows us to…
Studies of modular linear differential equations (MLDE) for the classification of rational CFT characters have been limited to the case where the coefficient functions (in monic form) have no poles, or poles at special points of moduli…
We introduce a new type of reduction of inversive difference polynomials that is associated with a partition of the basic set of automorphisms $\sigma$ and uses a generalization of the concept of effective order of a difference polynomial.…
This article introduces a new fast direct solver for linear systems arising out of wide range of applications, integral equations, multivariate statistics, radial basis interpolation, etc., to name a few. \emph{The highlight of this new…
Computation of polynomial relative invariants is a classical tool in algebra. Relative differential invariants are central for the equivalence problem of geometric structures. We address the fundamental problem of finite generation of their…
We propose POLAR, a novel radar-guided depth estimation method that introduces polynomial fitting to efficiently transform scaleless depth predictions from pretrained monocular depth estimation (MDE) models into metric depth maps. Unlike…
The notion of singular reduction modules, i.e., of singular modules of nonclassical (conditional) symmetry, of differential equations is introduced. It is shown that the derivation of nonclassical symmetries for differential equations can…
We prove two criteria for direct sum decomposability of homogeneous polynomials. For a homogeneous polynomial with a non-zero discriminant, we interpret direct sum decomposability of the polynomial in terms of factorization properties of…
One approach to parametric and adaptive model reduction is via the interpolation of orthogonal bases, subspaces or positive definite system matrices. In all these cases, the sampled inputs stem from matrix sets that feature a geometric…