  We analyze the performance of a linear-equality-constrained least-squares
(CLS) algorithm and its relaxed version, called rCLS, that is obtained via the
method of weighting. The rCLS algorithm solves an unconstrained least-squares
problem that is augmented by incorporating a weighted form of the linear
constraints. As a result, unlike the CLS algorithm, the rCLS algorithm is
amenable to our approach to performance analysis presented here, which is akin
to the energy-conservation-based methodology. Therefore, we initially inspect
the convergence properties and evaluate the precision of estimation as well as
satisfaction of the constraints for the rCLS algorithm in both mean and
mean-square senses. Afterwards, we examine the performance of the CLS algorithm
by evaluating the limiting performance of the rCLS algorithm as the relaxation
parameter (weight) approaches infinity. Numerical examples verify the accuracy
of the theoretical findings.
