Related papers: An implementation of Sub-CAD in Maple
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…
This paper presents the first systematic study on the fundamental problem of seeking optimal cell average decomposition (OCAD), which arises from constructing efficient high-order bound-preserving (BP) numerical methods within Zhang--Shu…
We study partial fraction decompositions (PFDs) in several variables using tools from commutative algebra. We give criteria for when a rational function with poles on a hyperplane arrangement has a desirable PFD. Our criteria are obtained…
It is well known that the variable ordering can be critical to the efficiency or even tractability of the cylindrical algebraic decomposition (CAD) algorithm. We propose new heuristics inspired by complexity analysis of CAD to choose the…
We introduce an algebraic multiscale method for two--dimensional problems. The method uses the generalized multiscale finite element method based on the quadrilateral nonconforming finite element spaces. Differently from the…
Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…
We describe our package PALP of C programs for calculations with lattice polytopes and applications to toric geometry, which is freely available on the internet. It contains routines for vertex and facet enumeration, computation of…
Cylindrical Algebraic Decomposition (CAD) is a key proof technique for formal verification of cyber-physical systems. CAD is computationally expensive, with worst-case doubly-exponential complexity. Selecting an optimal variable ordering is…
Geometric Deep Learning techniques have become a transformative force in the field of Computer-Aided Design (CAD), and have the potential to revolutionize how designers and engineers approach and enhance the design process. By harnessing…
Studies in thermodynamics often require the reduction of some first or second order partial derivatives in terms of a smaller basic set. A simple algorithm to perform such a reduction is presented here, together with a review of earlier…
In this paper, we describe a reliable symbolic computational algorithm for inverting general cyclic heptadiagonal matrices by using parallel computing along with recursion. The algorithm is implementable to the Computer Algebra System(CAS)…
In this note we give a precise statement and a detailed proof for reconstruction problem of weak bialgebra maps. As an application we characterize indecomposability of weak algebras in categorical setting.
Semidefinite Programming (SDP) provides tight lower bounds for Optimal Power Flow problems. However, solving large-scale SDP problems requires exploiting sparsity. In this paper, we experiment several clique decomposition algorithms that…
Lie symmetry analysis provides a general theoretical framework for investigating ordinary and partial differential equations. The theory is completely algorithmic even if it usually involves lengthy computations. For this reason, many…
Black-box model structures are dominated by large multivariate functions. Usually a generic basis function expansion is used, e.g. a polynomial basis, and the parameters of the function are tuned given the data. This is a pragmatic and…
We present a novel method for matrix completion, specifically designed for matrices where one dimension is significantly larger than the other. Our Columns Selected Matrix Completion (CSMC) method combines Column Subset Selection with…
Representation learning is typically applied to only one mode of a data matrix, either its rows or columns. Yet in many applications, there is an underlying geometry to both the rows and the columns. We propose utilizing this coupled…
This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and…
The optimal design of compounds through manipulating properties at the molecular level is often the key to considerable scientific advances and improved process systems performance. This paper highlights key trends, challenges, and…
We review the definition and main properties of differential subresultants in order to achieve their implementation in Maple, using the DEtools package. The focus is on computing GCRDs of ordinary differential operators with non necessarily…