TABLE OF CONTENTS It appears that Gauss and Doolittle applied the method only to symmetric equations. More recent authors, for example, Aitken, Banachiewicz, Dwyer, and Crout ... have emphasized the use of the method, or variations of it, in connection with non-symmetric problems ... Banachiewicz ... saw the point ... that the basic problem is really one of matrix factorization, or "decomposition" as he called it.
- PAUL S. DWYER, Linear Computations (1951)
Intolerable pivot-growth [with partial pivoting] is a phenomenon that happens only to numerical analysts who are looking for that phenomenon.
- WILLIAM M. KAHAN, Numerical Linear Algebra (1966)
By 1949 the major components of the Pilot ACE were complete and undergoing trials ... During 1951 a programme for solving simultaneous linear algebraic equations was used for the first time. 26th June, 1951 was a landmark in the history of the machine, for on that day it first rivalled alternative computing methods by yielding by 3 p.m. the solution to a set of 17 equations submitted the same morning.
- MICHAEL WOODGER, The History and Present Use of Digital Computers at the National Physical Laboratory (1958).
The closer one looks, the more subtle and remarkable Gaussian elimination appears.
- LLOYD N. TREFETHEN, Three Mysteries of Gaussian Elimination (1985)
We begin by giving a traditional description of Gaussian elimination (GE) for solving a linear system Ax = b, where 
is nonsingular.
The strategy of GE is to reduce...
