Computing the Higher k-Eigenfunctions by Monte Carlo Power Iteration: A Conjecture

Most Monte Carlo transport codes estimate the fundamental k-eigenfunction by means of a power iteration method. A modified power iteration method appears to generate the higher eigenfunctions for some Monte Carlo transport problems. This technical note describes the method as well as some plausibility arguments about why the method works. At this time, no formal proof exists to show that the method converges to the desired eigenfunction.