Cholesky and the Cholesky decomposition: a commemoration by an applied statistician

Abstract

Major André-Louis Cholesky was killed in action during the First World War on 31st August 1918. The
centenary of his death in action is an opportunity to pay tribute to this outstanding scientist. Linear regression methods
used in France at the time of his death are recalled. An early algorithm which Augustin-Louis Cauchy introduced to
alleviate the computational burden in multiple linear regression is revisited. This algorithm iteratively builds an upper-
triangular system of linear equations whose solution estimates the regression coefficients. It turns out that in the case
of least-squares the upper-triangular system which is constructed is exactly that obtained by applying a closely related
variant of the Cholesky decomposition to the normal equations.