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

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 approx...

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Bibliographic Details
Published in:Kybernetes 2008-02, Vol.37 (1), p.104-119
Main Authors: Mora, G., Cherruault, Y.
Format: Article
Language:English
Subjects:
Cybernetics
Euclidean space
Integration
Numerical flexibility
Polynomials
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Summary: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.
ISSN:0368-492X
1758-7883
DOI:10.1108/03684920810851023