相关论文: Symbolic Algorithm for Solving SLAEs with Heptadia…
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…
Machine-learning methods are gradually being adopted in a wide variety of social, economic, and scientific contexts, yet they are notorious for struggling with exact mathematics. A typical example is computer algebra, which includes tasks…
The numerical solution of large-scale Lyapunov matrix equations with symmetric banded data has so far received little attention in the rich literature on Lyapunov equations. We aim to contribute to this open problem by introducing two…
A rapid algorithm is derived for the Helmholtz--Hodge decomposition on the surface of the sphere in spherical coordinates. The algorithm uncouples modes of spherical harmonics with different absolute order, writes the conversion as…
A parallel algorithm for solving a series of matrix equations with a constant tridiagonal matrix and different right-hand sides is proposed and studied. The process of solving the problem is represented in two steps. The first preliminary…
Hyperbolic programming is the problem of computing the infimum of a linear function when restricted to the hyperbolicity cone of a hyperbolic polynomial, a generalization of semidefinite programming. We propose an approach based on symbolic…
A new polynomial preconditioner for symmetric complex linear systems based on Hermitian and skew-Hermitian splitting (HSS) for complex symmetric linear systems is herein presented. It applies to Conjugate Orthogonal Conjugate Gradient…
In numerical approaches to solving differential equations on a lattice, a representation of the derivative operator that correctly matches the continuum behaviour of functions of momentum up to the band limit must be non-local. We present…
To solve the spinor-spinor Bethe-Salpeter equation in Euclidean space we propose a novel method related to the use of hyperspherical harmonics. We suggest an appropriate extension to form a new basis of spin-angular harmonics that is…
Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…
We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…
Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…
In this paper we discuss Stochastic Differential-Algebraic Equations (SDAEs) and the asymptotic stability assessment for such systems via Lyapunov exponents (LEs). We focus on index-one SDAEs and their reformulation as ordinary stochastic…
This paper presents some algorithms in linear algebraic groups. These algorithms solve the word problem and compute the spinor norm for orthogonal groups. This gives us an algorithmic definition of the spinor norm. We compute the double…
In this paper we presents an algorithm for finding a solution of the linear nonhomogeneous quaternionic-valued differential equations. Moveover, several examples shows the feasibility of our algorithm.
When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions…
Solving symbolic reasoning problems that require compositionality and systematicity is considered one of the key ingredients of human intelligence. However, symbolic reasoning is still a great challenge for deep learning models, which often…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
This paper deals with the algorithmic aspects of solving feasibility problems of semidefinite programming (SDP), aka linear matrix inequalities (LMI). Since in some SDP instances all feasible solutions have irrational entries, numerical…
Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…