相关论文: Discrete Hybrid Polyharmonic Cubature Formulas wit…
We introduce a new type of cubature formula for the evaluation of an integral over the disk with respect to a weight function. The method is based on an analysis of the Fourier series of the weight function and a reduction of the bivariate…
The purpose of this work is to introduce a strategy for determining the nodes and weights of a low-cardinality positive cubature formula nearly exact for polynomials of a given degree over spherical polygons. In the numerical section we…
The goal of the paper is to describe essentially optimal cubature formulas on compact Riemannian manifolds which are exact on spaces of band- limited functions.
We derive new formulas for the high dimensional biharmonic potential acting on Gaussians or Gaussians times special polynomials. These formulas can be used to construct accurate cubature formulas of an arbitrary high order which are fast…
In the present paper we introduce a new concept of Hardy type space naturally defined on the Klein-Dirac quadric. We study different properties of the functions belonging to these spaces, in particular boundary value problems. We apply…
The present paper has a twofold contribution: first, we introduce a new concept of Hardy spaces on a multidimensional complexified annular domain which is closely related to the annulus of the Klein-Dirac quadric important in Conformal…
The paper develops applications of symmetric orbit functions, known from irreducible representations of simple Lie groups, in numerical analysis. It is shown that these functions have remarkable properties which yield to cubature formulas,…
We study cubature formulas for d-dimensional integrals with an arbitrary symmetric weight function of tensor product form. We present a construction that yields a high polynomial exactness: for fixed degree l=5 or l=7 and large dimension,…
In this article, a novel method to compute all discrete polyharmonic functions in the quarter plane for models with small steps, zero drift and a finite group is proposed. A similar method is then introduced for continuous polyharmonic…
A method is developed to compute analytically fully symmetric cubature rules on the triangle by using symmetric polynomials to express the two kinds of invariance inherent in these rules. Rules of degree up to 15, some of them new and of…
We construct an interpolatory high-order cubature rule to compute integrals of smooth functions over self-affine sets with respect to an invariant measure. The main difficulty is the computation of the cubature weights, which we…
The goal of the paper is to establish cubature formulas on combinatorial graphs. Two types of cubature formulas are developed. Cubature formulas of the first type are exact on spaces of variational splines on graphs. Since badlimited…
Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in \cite{LSX}. The main results consist of a new derivation of the Gaussian type cubature for the…
73 new cubature rules are found for three standard multidimensional integrals with spherically symmetric regions and weights, using direct search with a numerical zero-finder. All but four of the new rules have fewer integration points than…
We compute Poisson kernels for integer weight parameter standard weighted biharmonic operators in the unit disc with Dirichlet boundary conditions. The computations performed extend the supply of explicit examples of such kernels and…
Discrete orthogonality relations for Hall-Littlewood polynomials are employed, so as to derive cubature rules for the integration of homogeneous symmetric functions with respect to the density of the circular unitary ensemble (which…
The biharmonic equation with Dirichlet and Neumann boundary conditions discretized using the mixed finite element method and piecewise linear (with the possible exception of boundary triangles) finite elements on triangular elements has…
A new algebraic cubature formula of degree $2n+1$ for the product Chebyshev measure in the $d$-cube with $\approx n^d/2^{d-1}$ nodes is established. The new formula is then applied to polynomial hyperinterpolation of degree $n$ in three…
In numerical integration, cubature methods are effective, especially when the integrands can be well-approximated by known test functions, such as polynomials. However, the construction of cubature formulas has not generally been known, and…
In this article we furnish a new simple proof of a hard identity from the theory of cubature formulas via the method of coefficients.