Related papers: Discrete octonionic analysis: a unified approach t…
All but a few digital computers used for scientific computations have supported floating-point and digital arithmetic of rather limited numerical precision. The underlying assumptions were that the systems being studied were basically…
Continuing earlier investigations, we analyze the convergence of operator splitting procedures combined with spatial discretization and rational approximations.
The goal of this work is to characterize all second order difference operators of several variables that have discrete orthogonal polynomials as eigenfunctions. Under some mild assumptions, we give a complete solution of the problem.
An original approach to solving rather difficult probabilistic problems arising in studying the readout of random discrete fields and having no exact analytical solutions at the moment is proposed. Several algorithms for direct, iterative,…
We are interested in differential forms on mixed-dimensional geometries, in the sense of a domain containing sets of $d$-dimensional manifolds, structured hierarchically so that each $d$-dimensional manifold is contained in the boundary of…
Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…
We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…
We report on experience with an investigation of the analytic structure of the solution of certain algebraic complex equations. In particular the behavior of their series expansions around the origin is discussed. The investigation imposes…
We define an abstract framework called {\it discrete finite differences embedding} which can be used to obtain discrete analogue of formal functional relations in the spirit of category theory. For ordinary differential equations we exhibit…
On computers, discrete problems are solved instead of continuous ones. One must be sure that the solutions of the former problems, obtained in real time (i.e., when the stepsize h is not infinitesimal) are good approximations of the…
Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of…
The decomposition of the polynomials on the quaternionic unit sphere in $\Hd$ into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several…
The octagon abstract domain is a widely used numeric abstract domain expressing relational information between variables whilst being both computationally efficient and simple to implement. Each element of the domain is a system of…
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators.…
We use the octonion algebra to construct singular solutions of Hessian fully nonlinear uniformly elliptic equations in 21 or more dimensions. The regularity of these solutions is the least possible one. The same is proven for Isaacs…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
Dynamical systems are essential to model various phenomena in physics, finance, economics, and are also of current interest in machine learning. A central modeling task is investigating parameter sensitivity, whether tuning atmospheric…
Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…
Multidimensional noncommutative Laplace transforms over octonions are studied. Theorems about direct and inverse transforms and other properties of the Laplace transforms over the Cayley-Dickson algebras are proved. Applications to partial…