Dodgson’s Condensation Iterative Scheme for Evaluating Determinant of Square Matrix

Abstract

Dodgson’s condensation method has remained one of the remarkable methods employed for evaluating determinant of matrices of large order, and for solving large system of linear equation based on its suitability in combining with Cramer’s method. In the course of evaluating determinant using Dodgson’s condensation for a very large matrix one may run out of track in identifying the interior of the matrix that serve as a divisor for a particular condensed matrix. It is important to keep a check on this happenstance during computation by devising a suitable iteration scheme that implores Dodgson’s condensation processes so as to do away with the concept of Duplex Fraction recently introduced by a researcher in a bid to compute determinant of matrices with large order. Thus, the iteration scheme proposed generalizes this concept naturally and ultimately yields the value of the required determinant of the matrix without performing any elementary matrix operations on the row or column of the matrix.