Dave Robbins

A conjecture concerning approximate Dodgson condensation
Many people, including Dodgson himself, have noticed that the Dodgson condensation algorithm has potential problems with divisions by zero. When this occurs while computing over a field, it is not clear what to do next.

We will consider Dodgson condensation for determinants whose entries are integers mod pn, where p might be a small prime. Then there are a number of viable options for continuing if we need to divide by a non-invertible element. Empirically the resulting answers are often correct mod pm for surprisingly large m ≤ n.

For one particular algorithm it is possible to give a very sharp conjectural estimate, supported primarily by a lot of computational evidence, for the accuracy of the result.