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.
Keywords
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
Publisher
:Emerald Group Publishing Limited
Copyright © 2008, Emerald Group Publishing Limited