Perfect Gaussian Elimination
Martin Charles Golumbic
This chapter describes perfect gaussian elimination. Perfect elimination matrices are presented. Let M be a nonsingular n × n matrix with entries mij in some field (like the real numbers). One reduce M to the identity matrix I by repeatedly: (a) choosing a nonzero entry mij to act as pivot and (b) updating the matrix by using elementary row and column operations to change mij to 1 and to make all other entries in the ith row and jth column equal to 0. This familiar technique is called Gaussian elimination. When performing Gaussian elimination on a sparse matrix, an arbitrary choice of pivots may result in the filling in of some zero positions with nonzeros. One may ...
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