Smolyak's algorithm: a simple and accurate framework for the analysis of correlated log-normal power-sums

Authors:
Marco Di Renzo;Laura Imbriglio;Fabio Graziosi;Fortunato Santucci
Affiliations:
Institute for Digital Communications, University of Edinburgh, Edinburgh, UK;Dept. of Electrical and Information Engineering, the Center of Excellence DEWS, Univ. of L'Aquila, Italy;Dept. of Electrical and Information Engineering, the Center of Excellence DEWS, Univ. of L'Aquila, Italy;Dept. of Electrical and Information Engineering, the Center of Excellence DEWS, Univ. of L'Aquila, Italy
Venue:
IEEE Communications Letters
Year:
2009

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Abstract

The accurate analysis of Log-Normal power-sums requires the computation of multidimensional integrals with unknown closed-form. Typical approaches to numerically compute them are based on the full tensor-product formula, whose complexity raises exponentially with the number of summands. In this Letter, we propose a different method which is called Smolyak's algorithm. It belongs to the family of numerical integration techniques on sparse grids, and can be used in conjunction with several approximation methods for Log-Normal power-sums. Numerical results will show a complexity reduction greater than 99% without numerical accuracy degradation.