5: Gaussian Elimination
This article discusses the Gaussian elimination algorithm, one of the most fundamental and important numerical algorithms of all time. It is used to solve linear equations of the form
\[\mathbf{A} \vec{x} = \vec{b},\]
where \(\mathbf{A}\) is a known \(N\times N\) matrix, \(\vec{b}\) is a known vector of length \(N\), and \(\vec{x}\) is an unknown vector of length \(N\). The goal is to find \(\vec{x}\). The Gaussian elimination algorithm is implemented by Scipy's
scipy.linalg.solve
function.