Citations.bib

@article{niklasson2002,
  title={Expansion algorithm for the density matrix},
  author={Niklasson, Anders MN},
  journal={Physical Review B},
  volume={66},
  number={15},
  pages={155115},
  year={2002},
  publisher={APS}
}

@misc{truflandier2016communication,
  title={Communication: Generalized canonical purification for density matrix minimization},
  author={Truflandier, Lionel A and Dianzinga, Rivo M and Bowler, David R},
  year={2016},
  publisher={AIP Publishing}
}

@article{liang2003improved,
  title={Improved Fermi operator expansion methods for fast electronic structure calculations},
  author={Liang, WanZhen and Saravanan, Chandra and Shao, Yihan and Baer, Roi and Bell, Alexis T and Head-Gordon, Martin},
  journal={The Journal of chemical physics},
  volume={119},
  number={8},
  pages={4117--4125},
  year={2003},
  publisher={AIP}
}

@article{millam1997linear,
  title={Linear scaling conjugate gradient density matrix search as an alternative to diagonalization for first principles electronic structure calculations},
  author={Millam, John M and Scuseria, Gustavo E},
  journal={The Journal of chemical physics},
  volume={106},
  number={13},
  pages={5569--5577},
  year={1997},
  publisher={AIP}
}

@article{challacombe1999simplified,
  title={A simplified density matrix minimization for linear scaling self-consistent field theory},
  author={Challacombe, Matt},
  journal={The Journal of chemical physics},
  volume={110},
  number={5},
  pages={2332--2342},
  year={1999},
  publisher={AIP}
}

@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}
}

@misc{nicholas2008functions,
  title={Functions of matrices: theory and computation},
  author={Nicholas, J Higham},
  year={2008},
  publisher={SIAM}
}

@article{paterson1973number,
  title={On the number of nonscalar multiplications necessary to evaluate polynomials},
  author={Paterson, Michael S and Stockmeyer, Larry J},
  journal={SIAM Journal on Computing},
  volume={2},
  number={1},
  pages={60--66},
  year={1973},
  publisher={SIAM}
}

@article{higham2003computing,
  title={Computing the matrix cosine},
  author={Higham, Nicholas J and Smith, Matthew I},
  journal={Numerical Algorithms},
  volume={34},
  number={1},
  pages={13--26},
  year={2003},
  publisher={Springer}
}

@article{moler1978nineteen,
  title={Nineteen dubious ways to compute the exponential of a matrix},
  author={Moler, Cleve and Van Loan, Charles},
  journal={SIAM review},
  volume={20},
  number={4},
  pages={801--836},
  year={1978},
  publisher={SIAM}
}

@article{challacombe1999simplified,
  title={A simplified density matrix minimization for linear scaling self-consistent field theory},
  author={Challacombe, Matt},
  journal={The Journal of chemical physics},
  volume={110},
  number={5},
  pages={2332--2342},
  year={1999},
  publisher={AIP}
}

@article{rubensson2006determination,
  title={Determination of the chemical potential and HOMO/LUMO orbitals in density purification methods},
  author={Rubensson, Emanuel H and Jensen, Hans J{\o}rgen Aa},
  journal={Chemical physics letters},
  volume={432},
  number={4},
  pages={591--594},
  year={2006},
  publisher={Elsevier}
}

@article{niklasson2010trace,
  title={Trace correcting density matrix extrapolation in self-consistent geometry optimization},
  author={Niklasson, Anders MN and Challacombe, Matt and Tymczak, CJ and N{\'e}meth, K{\'a}roly},
  journal={The Journal of chemical physics},
  volume={132},
  number={12},
  pages={124104},
  year={2010},
  publisher={AIP}
}

@article{exner2002comparison,
  title={Comparison of nonlinear transformation methods for electron density approximation},
  author={Exner, Thomas E and Mezey, Paul G},
  journal={The Journal of Physical Chemistry A},
  volume={106},
  number={22},
  pages={5504--5509},
  year={2002},
  publisher={ACS Publications}
}

@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}
}

@book{boisvert1996matrix,
  title={The matrix market exchange formats: Initial design},
  author={Boisvert, Ronald F and Boisvert, Ronald F and Remington, Karin A},
  year={1996},
  publisher={US Department of Commerce, National Institute of Standards and Technology}
}

@article{jansik2007linear,
  title={Linear-scaling symmetric square-root decomposition of the overlap matrix},
  author={Jans{\'\i}k, Branislav and H{\o}st, Stinne and J{\o}rgensen, Poul and Olsen, Jeppe and Helgaker, Trygve},
  journal={The Journal of chemical physics},
  volume={126},
  number={12},
  pages={124104},
  year={2007},
  publisher={AIP}
}

@book{golub2012matrix,
  title={Matrix computations},
  author={Golub, Gene H and Van Loan, Charles F},
  volume={3},
  year={2012},
  publisher={JHU Press}
}

@article{imamura2011development,
  title={Development of a high performance eigensolver on the petascale next generation supercomputer system},
  author={Imamura, Toshiyuki and Yamada, Susumu and Machida, Masahiko},
  journal={Progress in Nuclear Science and Technology},
  volume={2},
  pages={643--650},
  year={2011}
}

@article{jay1999electronic,
  title={Electronic structure calculations for plane-wave codes without diagonalization},
  author={Jay, Laurent O and Kim, Hanchul and Saad, Yousef and Chelikowsky, James R},
  journal={Computer physics communications},
  volume={118},
  number={1},
  pages={21--30},
  year={1999},
  publisher={Amsterdam: North-Holland Pub. Co., 1969-}
}

@article{rubensson2011nonmonotonic,
  title={Nonmonotonic recursive polynomial expansions for linear scaling calculation of the density matrix},
  author={Rubensson, Emanuel H},
  journal={Journal of chemical theory and computation},
  volume={7},
  number={5},
  pages={1233--1236},
  year={2011},
  publisher={ACS Publications}
}

@article{aquilante2006fast,
  title={Fast noniterative orbital localization for large molecules},
  author={Aquilante, Francesco and Bondo Pedersen, Thomas and S{\'a}nchez de Mer{\'a}s, Alfredo and Koch, Henrik},
  journal={The Journal of chemical physics},
  volume={125},
  number={17},
  pages={174101},
  year={2006},
  publisher={American Institute of Physics}
}

@article{dawson2023complexity,
  title={Complexity reduction in density functional theory: 
         Locality in space and energy},
  author={Dawson, William and Kawashima, Eisuke and Ratcliff, 
          Laura E and Kamiya, Muneaki and Genovese, Luigi and 
          Nakajima, Takahito},
  journal={The Journal of Chemical Physics},
  volume={158},
  number={16},
  year={2023},
  publisher={AIP Publishing}
}