IJPAM: Volume 22, No. 1 (2005)

DIMENSIONALITY REDUCING MULTIPLE INTEGRALS
BY ALPHA-DENSE CURVES

G. Mora$^1$, G. Mora-Porta$^2$
$^1$Departamento de Análisis Matemático
Universidad de Alicante
Alicante, 03080, SPAIN
e-mail: gaspar.mora@ua.es
$^2$D.I.S.C.A. Universidad Politécnica de Valencia
Valencia, 46022, Camino de Vera s/n, SPAIN
e-mail: gmora@gap.upv.es


Abstract.We approximate the multiple integral of a non-negative real function $f$ of class $C^{1}$ on the unit cube $\left[ 0,1\right]
^{n},n\geq 2,$ by a simple one on the interval $\left[ -1,1\right] $ by using a technique of densification of the region of quadrature. The curve that densifies is an $\alpha $-dense curve called cosines curve. The integrand of the simple integral depends, as that of $\left[ 8\right] $, on the Chebyshev polynomial of second kind. An estimation on the error generated by this reduction is also settled.

Received: June 9, 2005

AMS Subject Classification: 33F05, 12E10

Key Words and Phrases: alpha-dense curves, Chebyshev polynomials, numerical integration

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 22
Issue: 1