This paper seeks to present an original method for transforming multiple integrals into simple integrals.
This can be done by using α‐dense curves invented by Y. Cherruault and A. Guillez at the beginning of the 1980s.
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.
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.
The paper presents an original method for transforming integrals into simple integrals.
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/10.1108/03684920810851023Download as .RIS
Emerald Group Publishing Limited
Copyright © 2008, Emerald Group Publishing Limited