相关论文: Application of multivariate splines to discrete ma…
In this paper, we use multivariate splines to investigate the volume of polytopes. We first present an explicit formula for the multivariate truncated power, which can be considered as a dual version of the famous Brion's formula for the…
Based on discrete truncated powers, the beautiful Popoviciu's formulation for restricted integer partition function is generalized. An explicit formulation for two dimensional multivariate truncated power functions is presented. Therefore,…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
In this paper, we explore the interrelationship between Eulerian numbers and B splines. Specifically, using B splines, we give the explicit formulas of the refined Eulerian numbers, and descents polynomials. Moreover, we prove that the…
The simple product formulae for derivatives of scalar functions raised to different powers are generalized for functions which take values in the set of symmetric positive definite matrices. These formulae are fundamental in derivation of…
The purpose of this work is to illustrate how the theory of Muckenhoupt weights, Muckenhoupt weighted Sobolev spaces and the corresponding weighted norm inequalities can be used in the analysis and discretization of PDE constrained…
In the paper, we give methods of construction of dual bases for the B-spline basis and truncated power basis. Explicit formulas for the dual B-spline basis are obtained using the Legendre-like orthogonal basis of the polynomial spline space…
Multivariate piecewise polynomial functions (or splines) on polyhedral complexes have been extensively studied over the past decades and find applications in diverse areas of applied mathematics including numerical analysis, approximation…
The problem of iterated partial summations is solved for some discrete distributions defined on discrete supports. The power method, usually used as a computational approach to finding matrix eigenvalues and eigenvectors, is in some cases…
We consider a non-polynomial cubic spline to develop the classes of methods for the numerical solution of singularly perturbed two-point boundary value problems. The proposed methods are second and fourth order accurate and applicable to…
Recently in joint work with E. Sert, we proved sharp boundedness results on discrete fractional integral operators along binary quadratic forms. Present work vastly enhances the scope of those results by extending boundedness to bivariate…
We propose a collocation method based on multivariate polynomial splines over triangulation or tetrahedralization for the numerical solution of partial differential equations. We start with a detailed explanation of the method for the…
We use trivariate spline functions for the numerical solution of the Dirichlet problem of the 3D elliptic Monge-Amp\'ere equation. Mainly we use the spline collocation method introduced in [SIAM J. Numerical Analysis, 2405-2434,2022] to…
Bilinear forms for some nonlinear partial difference equations(discrete soliton equations) are derived based on the results of singularity confinement. Using the bilinear forms, the N-soliton and algebraic solutions of the discrete…
On the basis of loop group decompositions (Birkhoff decompositions), we give a discrete version of the nonlinear d'Alembert formula, a method of separation of variables of difference equations, for discrete constant negative Gauss curvature…
We introduce discrete analogues of the exponential, sine, and cosine functions. Then using a discrete trigonometric version of a non-polynomial divided difference, we define discrete analogues of the trigonometric B-splines. We derive a…
We use a discrete multiscale analysis to study the asymptotic integrability of differential-difference equations. In particular, we show that multiscale perturbation techniques provide an analytic tool to derive necessary integrability…
This paper focuses on the strong convergence of the truncated $\theta$-Milstein method for a class of nonautonomous stochastic differential delay equations whose drift and diffusion coefficients can grow polynomially. The convergence rate,…
Given a multi-variable polynomial, there is an associated divided symmetrization (in particular turning it into a symmetric function). Postinkov has found the volume of a permutohedron as a divided symmetrization (DS) of the power of a…
We give an elementary introduction to some recent polyhedral techniques for understanding and solving systems of multivariate polynomial equations. We provide numerous concrete examples and illustrations, and assume no background in…