Generalizing Dodgson's method: a "double-crossing" approach to computing determinants

TL;DR

This paper introduces a 'double-crossing' generalization of Dodgson's determinant computation method, overcoming its failure when encountering zero entries, thus broadening its applicability.

Contribution

The paper presents a novel 'double-crossing' approach that extends Dodgson's method to handle cases with zero interior entries, improving its robustness.

Findings

Successfully generalizes Dodgson's method

Provides a workaround for zero-entry failures

Enhances determinant computation reliability

Abstract

Dodgson's method of computing determinants was recently revisited in a paper that appeared in the College Math Journal. The method is attractive, but fails if an interior entry of an intermediate matrix has the value zero. This paper reviews the structure of Dodgson's method and introduces a generalization, called a "double-crossing" method, that provides a workaround to the failure for many interesting cases.