A Geometric Analysis of Gaussian Elimination. I
The algorithm known as Gaussian elimination (GE) is fully understood in an exact-arithmetic environment. But in the finite-precision environment of computers, a full understanding of GE has been somewhat elusive. Heretofore, the analysis of this popular and important algorithm has been primarily from a numerical perspective. This paper seeks to analyze GE from a geometric perspective, and by so doing, (1) confirm the classical numerical analysis and (2) demonstrate a new level of understanding through the Euclidean geometry of GE.
Poole, George; and Neal, Larry. 1991. A Geometric Analysis of Gaussian Elimination. I. Linear Algebra and Its Applications. Vol.149(C). 249-272. https://doi.org/10.1016/0024-3795(91)90337-V ISSN: 0024-3795