Comparison of some variational strategies used in field theory

Recently two variational strategies have been applied to the standard and linear δ expansions for quantum field theories. These strategies, both of which improve the accuracy of the expansions, have the property that for N self-interacting fields at large N the lowest-order δ expansion improved by the variational strategy gives the exact large-N result. In this article, we study, in the context of supersymmetric quantum mechanics, the numerical accuracy of the improved δ expansions when calculated to large order in δ and compare them with the accuracy of the large-N expansion. We find that the usual δ expansion is the most accurate, followed by the linear δ expansion. The large-N expansion, analytically continued to N=1, is the least accurate method of the three