Concerning low-order spectral coefficients

Abstract

Standard methods for Rademacher-Walsh spectral coefficients involve n2n operations to deduce the complete spectrum for a function of n variables. The number of operations required to evaluate only the low-order coefficients is discussed in this paper and an exact result for the number of operations in the evaluation of all coefficients of orders up to z (for some z less than n) is deduced. Although the number of operations is considerably reduced, data structures of greater complexity are required.