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

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.