  Random walks are frequently used as a model for very diverse physical
phenomena. The Monte Carlo method is a versatile tool for the study of the
properties of the systems modelled as random walks. Often, each walker is
associated with a statistical weight, used in the estimation of observable
quantities. Weights are typically assumed to be positive; nonetheless, some
applications require the use of positive and negative weights or complex
weights, and often pose particular challenges with convergence. In this paper,
we examine such a case from the field of nuclear reactor physics, where the
negative particle weights prevent the power iteration algorithm from converging
on the sought fundamental eigenstate of the Boltzmann transport equation. We
demonstrate how the use of weight cancellation allows convergence on the
physical eigenstate. To this end, we develop a novel method to perform weight
cancellation in an exact manner, in three spatial dimensions. The viability of
this algorithm is then demonstrated on a reactor physics problem.
