Related papers: Solving Decomposable Sparse Systems
Sparse (or toric) elimination exploits the structure of polynomials by measuring their complexity in terms of Newton polytopes instead of total degree. The sparse, or Newton, resultant generalizes the classical homogeneous resultant and its…
We present a Galois theory of parameterized linear differential equations where the Galois groups are linear differential algebraic groups, that is, groups of matrices whose entries are functions of the parameters and satisfy a set of…
A large family of linear, usually overdetermined, systems of partial differential equations that admit a multiplication of solutions, i.e, a bi-linear and commutative mapping on the solution space, is studied. This family of PDE's contains…
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…
We examine whether it is possible to realize finite groups $G$ as Galois groups of minimally tamely ramified extensions of $\mathbb{Q}$ and also specify both the inertia groups and the further decomposition of the ramified primes.
We consider some examples of superintegrable system which were recently isolated through a differential Galois group analysis. The identity of these systems is clarified and the corresponding Poisson algebras derived.
In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new…
We present a new probabilistic algorithm that characterizes the equidimensional components of the affine algebraic variety defined by an arbitrary sparse polynomial system with prescribed supports. For each equidimensional component, the…
We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…
We exhibit a probabilistic symbolic algorithm for solving zero-dimensional sparse systems. Our algorithm combines a symbolic homotopy procedure, based on a flat deformation of a certain morphism of affine varieties, with the polyhedral…
We propose an approach for the computation of multi-parameter families of Galois extensions with prescribed ramification type. More precisely, we combine existing deformation and interpolation techniques with recently developed strong tools…
This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…
Noncommutative harmonic analysis is used to solve a nonparametric estimation problem stated in terms of compound Poisson processes on compact Lie groups. This problem of decompounding is a generalization of a similar classical problem. The…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of…
This paper is concerned with the problem of finding a quadratic common Lyapunov function for a family of stable linear systems. We present gradient iteration algorithms which give deterministic convergence for finite system families and…
We present a fast randomized algorithm that computes a low rank LU decomposition. Our algorithm uses random projections type techniques to efficiently compute a low rank approximation of large matrices. The randomized LU algorithm can be…
A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…
We study a class of overdetermined algebraic systems of equations. We prove that the number of distinct solutions equals to the maximal possible if and only if certain matrices are commuting and semisimple. This gives a characterization of…
This paper deals with the polynomial linear system solving with errors (PLSwE) problem. Specifically, we focus on the evaluation-interpolation technique for solving polynomial linear systems and we assume that errors can occur in the…