A new approach to the reduction of multiple integrals to simple ones using Chebyshev's kernels

Abstract

Purpose

This paper seeks to present an original method for transforming multiple integrals into simple integrals.

Design/methodology/approach

This can be done by using α‐dense curves invented by Y. Cherruault and A. Guillez at the beginning of the 1980s.

Findings

These curves allow one to approximate the space Rⁿ (or a compact of Rⁿ) with the accuracy α. They generalize fractal curves of Mandelbrobdt. They can be applied to global optimization where the multivariables functional is transformed into a functional depending on a single variable.

Practical implications

Applied to a multiple integral, the α‐dense curves using Chebyshev's kernels permit one to obtain a simple integral approximating the multiple integral. The accuracy depends on the choice of α.

Originality/value

The paper presents an original method for transforming integrals into simple integrals.

Citation

Mora, G. and Cherruault, Y. (2008), "A new approach to the reduction of multiple integrals to simple ones using Chebyshev's kernels", Kybernetes, Vol. 37 No. 1, pp. 104-119. https://doi.org/10.1108/03684920810851023