Aversion of Inversion

Oren Rippel Computation Leave a Comment

[latexpage] In the spirit of Ryan’s most recent post, I will discuss a fundamental snippet from numerical linear algebra that facilitates computation for the same price of not facilitating it. In our everyday lives, we often come across theoretical expressions that involve matrix inverses stapled to vectors, such as $\Omega^{-1}\mathbf{x}$ with $\Omega\in\mathbb{R}^{n\times n}, \mathbf{x}\in\mathbb{R}^n$. When we proceed to code this up, it is very tempting to first compute $\Omega^{-1}$. Resist doing this! There are several points for why there is no point to actually find an explicit, tangible inverse.