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5: Gaussian Elimination

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  • 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.

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