Abstract
The eigenvalue moment method (EMM), a linear-programming (LP) based technique for generating converging bounds to quantum eigenenergies, is reformulated as an iterative dynamical system (DS). Important convexity properties are uncovered significantly impacting the theoretical and computational implementation of the EMM program. In particular, whereas the LP-based EMM formulation (LP-EMM) can require the generation and storage of many inequalities [up to several thousand for a 10-missing moment problem (${\mathit{m}}_{\mathit{s}}$=10)], the dynamical-system formulation (DS-EMM) generates a reduced set of inequalities [of order O(${\mathit{m}}_{\mathit{s}}$+1)]. This is made possible by replacing the LP generation of deep interior points (DIP's) by a Newton iteration process. The latter generates an optimal set of DIP's sufficient to determine the existence or nonexistence of the relevant missing moment polytopes. The general DS-EMM theory is presented together with numerical examples.
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