  The main theme of this paper is error analysis for approximations derived
from two variants of dimensional decomposition of a multivariate function: the
referential dimensional decomposition (RDD) and analysis-of-variance
dimensional decomposition (ADD). New formulae are presented for the lower and
upper bounds of the expected errors committed by bivariately and arbitrarily
truncated RDD approximations when the reference point is selected randomly,
thereby facilitating a means for weighing RDD against ADD approximations. The
formulae reveal that the expected error from the S-variate RDD approximation of
a function of N variables, where $0 \le S < N < \infty$, is at least $2^{S+1}$
times greater than the error from the S-variate ADD approximation.
Consequently, ADD approximations are exceedingly more precise than RDD
approximations. The analysis also finds the RDD approximation to be sub-optimal
for an arbitrarily selected reference point, whereas the ADD approximation
always results in minimum error. Therefore, the RDD approximation should be
used with caution.

Numerical Analysis