Fast calculation of coefficients in the Smolyak algorithm

摘要: For many numerical problems involving smooth multivariate functions on d-cubes, the so-called Smolyak algorithm (or Boolean method, sparse grid etc.) has proved to be very useful. The final form of (see equation (12) below) requires functional evaluation as well computation coefficients. latter can done in different ways that may have considerable influence total cost algorithm. In this paper, we try diminish far possible. example, present an for integration problem reduces time calculation and exposition coefficients such a way increasing dimension, is small compared dn, where n number involved function values.