Cubature formulas of multivariate polynomials arising from symmetric orbit functions

Abstract

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, approximating a weighted integral of any function by a weighted finite sum of function values, in connection with any simple Lie group. The cubature formulas are specialized for simple Lie groups of rank two. An optimal approximation of any function by multivariate polynomials arising from symmetric orbit functions is discussed.

19 pages, 4 figures

References in corpus (5)

• Antisymmetric Orbit Functions
• E-Orbit Functions
• Orthogonality within the Families of C-, S-, and E-Functions of Any Compact Semisimple Lie Group
• Generalized discrete orbit function transforms of affine Weyl groups
• Computing the demagnetizing tensor for finite difference micromagnetic simulations via numerical integration

Cited by in corpus (9)

• On E-Discretization of Tori of Compact Simple Lie Groups: II
• Discrete cosine and sine transforms generalized to honeycomb lattice
• Exact cubature rules for symmetric functions
• On construction of finite averaging sets for $SL(2,\mathbb{C})$ via its Cartan decomposition
• Cubature rules for unitary Jacobi ensembles
• Cubature rules from Hall-Littlewood polynomials
• Fast cosine transform for FCC lattices
• High-Order Quadrature on Multi-Component Domains Implicitly Defined by Multivariate Polynomials
• FFT and orthogonal discrete transform on weight lattices of semi-simple Lie groups