Exact cubature rules for symmetric functions

Autor:	van Diejen, J. F., Emsiz, E.
Rok vydání:	2019
Předmět:	Mathematics - Numerical Analysis Mathematics - Classical Analysis and ODEs Mathematics - Combinatorics 65D32 05E05 15B52 33C52 33D52 65T40
Zdroj:	Math. Comp. 88 (2019), no. 317, 1229-1249
Druh dokumentu:	Working Paper
DOI:	10.1090/mcom/3380
Popis:	We employ a multivariate extension of the Gauss quadrature formula, originally due to Berens, Schmid and Xu [BSX95], so as to derive cubature rules for the integration of symmetric functions over hypercubes (or infinite limiting degenerations thereof) with respect to the densities of unitary random matrix ensembles. Our main application concerns the explicit implementation of a class of cubature rules associated with the Bernstein-Szeg\"o polynomials, which permit the exact integration of symmetric rational functions with prescribed poles at coordinate hyperplanes against unitary circular Jacobi distributions stemming from the Haar measures on the symplectic and the orthogonal groups. Comment: 20 pages, LaTeX
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1903.00868 Zobrazit plný text záznamu View this record from Arxiv