Slow Exponential Growth for Clenshaw Curtis Sparse Grids

When Clenshaw Curtis rules are used to form a sparse grid, the orders of the underlying 1D factor rules form an exponential series. Even for a relatively low level, the 1D order growth is unnecessary, and is reflected in a noticeable cost in the order of the resulting sparse grid. We consider the effect of using the Clenshaw Curtis rules in a way that maintains the nestedness but delays their exponential growth so effectively that it becomes essentially linear. This restraint, in turn, brings down the cost of the sparse grids while entirely meeting the desired precision levels.