# A note on Dodgson's determinant condensation algorithm

## TL;DR

This paper discusses a symbolic modification of Dodgson's determinant condensation algorithm, addressing its shortcomings and analyzing its sensitivity to initial matrix configurations through numerical experiments.

## Contribution

It introduces a symbolic algorithm to improve Dodgson's method and examines its limitations and sensitivity issues.

## Key findings

- The symbolic algorithm can overcome some shortcomings of the original method.
- The modified algorithm is highly sensitive to initial matrix configurations.
- Numerical experiments reveal the limitations and potential of the symbolic approach.

## Abstract

Recently, the Dodgson's determinant condensation algorithm was revisited in many papers [College Math. Journal 42(1)(2011): 43--54, College Math. Journal 38(2)(2007): 85--95, Math Horizons 14(2)(2006): 12--15},etc.]. This method is attractive, but there also exist some shortcomings. In this paper, a symbolic algorithm and the corresponding problems are discussed to overcome these shortcomings. Numerical experiments show that this symbolic modified algorithm has highly sensitivity on initial configuration of the matrix in condensation process.