  Contour integration schemes are a valuable tool for the solution of difficult
interior eigenvalue problems. However, the solution of many large linear
systems with multiple right hand sides may prove a prohibitive computational
expense. The number of right hand sides, and thus, computational cost may be
reduced if the projected subspace is created using multiple moments. In this
work, we explore heuristics for the choice and application of moments with
respect to various other important parameters in a contour integration scheme.
We provide evidence for the expected performance, accuracy, and robustness of
various schemes, showing that good heuristic choices can provide a scheme
featuring good properties in all three of these measures.
