Matrix Inverse

Overview

The matrix inverse can be computed using Hotelling's method.

Method

For a more detailed introduction to Hotelling's method, please see my blog post: https://william-dawson.github.io/blog/method/2017/08/21/hotelling.html

How To Cite

For Hotelling's method in the context of electronic structure calculations, I think it is appropriate cite the following paper:

@article{palser1998canonical,
title={Canonical purification of the density matrix in electronic-structure theory},
author={Palser, Adam HR and Manolopoulos, David E},
journal={Physical Review B},
volume={58},
number={19},
pages={12704},
year={1998},
publisher={APS}
}

Of course, the original work of Dr. Harold Hotelling should be recognized

@article{hotelling1943some,
title={Some new methods in matrix calculation},
author={Hotelling, Harold},
journal={The Annals of Mathematical Statistics},
volume={14},
number={1},
pages={1--34},
year={1943},
publisher={JSTOR}
}

There is also a very nice later paper by Dr. Taisuke Ozaki:

@article{ozaki2001efficient,
title={Efficient recursion method for inverting an overlap matrix},
author={Ozaki, T},
journal={Physical Review B},
volume={64},
number={19},
pages={195110},
year={2001},
publisher={APS}
}