This paper reviews some recent developments in interpolation, interpolatory cubature, and high-order numerical integration on the sphere $S^2$. In interpolatory (polynomial) cubature the integrand is approximated by the interpolating polynomial (in the space $\\mathbb{P}_n$ of all spherical polynomials up to a fixed degree $n$) with respect to an appropriate pointset, and the integral of the interpolating polynomial is then evaluated exactly. Formulated in terms of Lagrange polynomials, this leads to a cubature rule with the weights given by integrals over the respective Lagrange polynomials. The quality of such cubature rules depends heavily on the pointset. In this paper we discuss so-called extremal pointsets, which are pointsets for whi...
In this paper we survey hyperinterpolation on the sphere $\\mathbb{S}^d$, $d\\geq 2$. The hyperinter...
This paper is concerned with numerical integration on the unit sphere $S^r$ of dimension $r\\geq 2$ ...
We study numerical integration on the unit sphere S2 ⊆ R3 using equal weight quadrature rules, where...
This paper reviews some recent developments in cubature over the sphere $S^2$ for functions in Sobol...
AbstractThis paper studies numerical integration (or cubature) over the unit sphere S2⊂R3 for functi...
This paper studies numerical integration (or cubature) over the unit sphere $S^2\\subset\\mathbb{R}^...
AbstractWe construct interpolatory cubature rules on the two-dimensional sphere, using the fundament...
This chapter is concerned with numerical integration over the unit sphere S2 ⊂ ℝ;3. We first discuss...
This paper studies the problem of numerical integration over the unit sphere $S^2\\subseteq\\mathbb{...
AbstractThis paper studies a generalization of polynomial interpolation: given a continuous function...
AbstractThis paper studies a generalization of polynomial interpolation: given a continuous function...
Abstract: In [3] we studied some interpolatory cubature formulas associated to a fundamental system ...
AbstractThis paper studies numerical integration (or cubature) over the unit sphere S2⊂R3 for functi...
Using some recent results on subperiodic trigonometric interpolation and quadrature, and the theor...
AbstractWe construct interpolatory cubature rules on the two-dimensional sphere, using the fundament...
In this paper we survey hyperinterpolation on the sphere $\\mathbb{S}^d$, $d\\geq 2$. The hyperinter...
This paper is concerned with numerical integration on the unit sphere $S^r$ of dimension $r\\geq 2$ ...
We study numerical integration on the unit sphere S2 ⊆ R3 using equal weight quadrature rules, where...
This paper reviews some recent developments in cubature over the sphere $S^2$ for functions in Sobol...
AbstractThis paper studies numerical integration (or cubature) over the unit sphere S2⊂R3 for functi...
This paper studies numerical integration (or cubature) over the unit sphere $S^2\\subset\\mathbb{R}^...
AbstractWe construct interpolatory cubature rules on the two-dimensional sphere, using the fundament...
This chapter is concerned with numerical integration over the unit sphere S2 ⊂ ℝ;3. We first discuss...
This paper studies the problem of numerical integration over the unit sphere $S^2\\subseteq\\mathbb{...
AbstractThis paper studies a generalization of polynomial interpolation: given a continuous function...
AbstractThis paper studies a generalization of polynomial interpolation: given a continuous function...
Abstract: In [3] we studied some interpolatory cubature formulas associated to a fundamental system ...
AbstractThis paper studies numerical integration (or cubature) over the unit sphere S2⊂R3 for functi...
Using some recent results on subperiodic trigonometric interpolation and quadrature, and the theor...
AbstractWe construct interpolatory cubature rules on the two-dimensional sphere, using the fundament...
In this paper we survey hyperinterpolation on the sphere $\\mathbb{S}^d$, $d\\geq 2$. The hyperinter...
This paper is concerned with numerical integration on the unit sphere $S^r$ of dimension $r\\geq 2$ ...
We study numerical integration on the unit sphere S2 ⊆ R3 using equal weight quadrature rules, where...