  There has been renewed interest in the exploitation of Barta's configuration
space theorem (BCST, (1937)) which bounds the ground state energy. Mouchet's
(2005) BCST analysis is based on gradient optimization (GO). However, it
overlooks significant difficulties: (i) appearance of multi-extrema; (ii)
inefficiency of GO for stiff (singular perturbation/strong coupling) problems;
(iii) the nonexistence of a systematic procedure for arbitrarily improving the
bounds. These deficiencies can be corrected by transforming BCST into a
moments' representation equivalent, and exploiting a generalization of the
Eigenvalue Moment Method (EMM), within the context of the well known
Generalized Eigenvalue Problem (GEP), as developed here.
