main.bib

The numerical linear algebra textbook
@book{golub2012matrix,
  title={Matrix Computations},
  author={Golub, Gene H and Van Loan, Charles F},
  year={2013},
  edition={4},
  publisher={The John Hopkins University Press}
}

LAPACK Working Note 286 for triangular eigensolver (ZTREVC)
@incollection{gates2014accelerating,
  title={Accelerating computation of eigenvectors in the dense nonsymmetric eigenvalue problem},
  author={Gates, Mark and Haidar, Azzam and Dongarra, Jack},
  booktitle={High Performance Computing for Computational Science--VECPAR 2014},
  pages={182--191},
  year={2014},
  publisher={Springer}
}

LAPACK safe triangular solve (ZLATRS)
@book{anderson1991robust,
  title={Robust triangular solves for use in condition estimation},
  author={Anderson, Edward},
  year={1991},
  publisher={University of Tennessee. Computer Science Department}
}

Level 1 BLAS
@article{lawson1979basic,
  title={Basic linear algebra subprograms for {Fortran} usage},
  author={Lawson, Chuck L and Hanson, Richard J. and Kincaid, David R and Krogh, Fred T.},
  journal={ACM Transactions on Mathematical Software},
  volume={5},
  number={3},
  pages={308--323},
  year={1979},
  publisher={ACM}
}

Level 2 BLAS
@article{dongarra1988extended,
  title={An extended set of {Fortran} basic linear algebra subroutines},
  author={Dongarra, Jack J and Du Croz, Jeremy and Hammarling, Sven and Hanson, Richard J},
  journal={ACM Transactions on Mathematical Software},
  volume={14},
  number={1},
  pages={1--17},
  year={1988},
  publisher={ACM}
}
@article{dongarra1988algorithm,
  title={Algorithm 656: an extended set of basic linear algebra
                  subprograms: model implementation and test programs},
  author={Dongarra, Jack J and Du Croz, Jeremy and Hammarling, Sven
                  and Hanson, Richard J},
  journal={ACM Transactions on Mathematical Software},
  volume={14},
  number={1},
  pages={18--32},
  year={1988},
  publisher={ACM}
}

Level 3 BLAS
@article{dongarra1990set,
  title={A set of level 3 basic linear algebra subprograms},
  author={Dongarra, Jack J and Du Croz, Jeremy and Hammarling, Sven and Duff, Iain S},
  journal={ACM Transactions on Mathematical Software},
  volume={16},
  number={1},
  pages={1--17},
  year={1990},
  publisher={ACM}
}
@article{dongarra1990algorithm,
  title={Algorithm 679: A set of level 3 basic linear algebra subprograms: model implementation and test programs},
  author={Dongarra, Jack J and Cruz, Jermey Du and Hammerling, Sven and Duff, Iain S},
  journal={ACM Transactions on Mathematical Software},
  volume={16},
  number={1},
  pages={18--28},
  year={1990},
  publisher={ACM}
}

ATLAS
@article{whaley2005minimizing,
  title={Minimizing development and maintenance costs in supporting persistently optimized {BLAS}},
  author={Whaley, R Clint and Petitet, Antoine},
  journal={Software: Practice and Experience},
  volume={35},
  number={2},
  pages={101--121},
  year={2005},
  publisher={Wiley Online Library}
}

OpenBLAS
@inproceedings{zhang2012model,
  title={Model-driven level 3 {BLAS} performance optimization on {Loongson 3A} processor},
  author={Zhang, Xianyi and Wang, Qian and Zhang, Yunquan},
  booktitle={2012 IEEE 18th International Conference on Parallel and
                  Distributed Systems},
  pages={684--691},
  year={2012},
  organization={IEEE}
}
@inproceedings{wang2013augem,
  title={{AUGEM}: automatically generate high performance dense linear algebra kernels on x86 {CPUs}},
  author={Wang, Qian and Zhang, Xianyi and Zhang, Yunquan and Yi, Qing},
  booktitle={Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis},
  pages={25},
  year={2013},
  organization={ACM}
}

Outline paper for Elemental package
@article{poulson2013elemental,
  title={Elemental: A new framework for distributed memory dense matrix computations},
  author={Poulson, Jack and Marker, Bryan and Van de Geijn, Robert A and Hammond, Jeff R and Romero, Nichols A},
  journal={ACM Transactions on Mathematical Software},
  volume={39},
  number={2},
  pages={13},
  year={2013},
  publisher={ACM}
}

EigTool
@misc{wright2002eigtool, 
author={Thomas G Wright},
title={{EigTool}},
howpublished={\url{http://www.comlab.ox.ac.uk/pseudospectra/eigtool/}},
year={2002}
}
@article{wright2001large,
  title={Large-scale computation of pseudospectra using {ARPACK} and eigs},
  author={Wright, Thomas G and Trefethen, Lloyd N},
  journal={SIAM Journal on Scientific Computing},
  volume={23},
  number={2},
  pages={591--605},
  year={2001},
  publisher={SIAM}
}

Review article for pseudospectra
@article{trefethen1999computation,
  title={Computation of pseudospectra},
    author={Trefethen, Lloyd N},
      journal={Acta Numerica},
        volume={8},
          pages={247--295},
            year={1999},
              publisher={Cambridge University Press}
              }

Book on pseudospectra              
@book{trefethen2005spectra,
  title={Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators},
  author={Trefethen, Lloyd Nicholas and Embree, Mark},
  year={2005},
  publisher={Princeton University Press}
}

Van Loan-Lui algorithm for computing pseudospectra
@techreport{van1984near,
  title={How near is a stable matrix to an unstable matrix?},
  author={Van Loan, Charles},
  year={1984},
  institution={Cornell University}
}
@article{lui1997computation,
  title={Computation of pseudospectra by continuation},
  author={Lui, SH},
  journal={SIAM Journal on Scientific Computing},
  volume={18},
  number={2},
  pages={565--573},
  year={1997},
  publisher={SIAM}
}

Multishift QR algorithm (LAPACK ZHSEQR)
@article{braman2002multishift1,
  title={The multishift {QR} algorithm. part {I}: Maintaining well-focused shifts and level 3 performance},
  author={Braman, Karen and Byers, Ralph and Mathias, Roy},
  journal={SIAM Journal on Matrix Analysis and Applications},
  volume={23},
  number={4},
  pages={929--947},
  year={2002},
  publisher={SIAM}
}
@article{braman2002multishift2,
  title={The multishift {QR} algorithm. Part {II}: Aggressive early deflation},
  author={Braman, Karen and Byers, Ralph and Mathias, Roy},
  journal={SIAM Journal on Matrix Analysis and Applications},
  volume={23},
  number={4},
  pages={948--973},
  year={2002},
  publisher={SIAM}
}

Blocked Hessenberg reduction (LAPACK GEHRD)
@article{quintana2006improving,
  title={Improving the performance of reduction to {Hessenberg} form},
  author={Quintana-Ort{\'\i}, Gregorio and Geijn, Robert van de},
  journal={ACM Transactions on Mathematical Software},
  volume={32},
  number={2},
  pages={180--194},
  year={2006},
  publisher={ACM}
}
@article{bischof1987wy,
  title={The {WY} representation for products of {Householder} matrices},
  author={Bischof, Christian and Van Loan, Charles},
  journal={SIAM Journal on Scientific and Statistical Computing},
  volume={8},
  number={1},
  pages={s2--s13},
  year={1987},
  publisher={SIAM}
}
@book{bischof1993summary,
  title={A summary of block schemes for reducing a general matrix to {Hessenberg} form},
  author={Bischof, Christian},
  year={1993},
  publisher={Argonne National Laboratory}
}

LAPACK
@book{anderson1999lapack,
      AUTHOR = {Anderson, E and Bai, Z and Bischof, C and
                Blackford, S and Demmel, J and Dongarra, J and
                Du Croz, J and Greenbaum, A and Hammarling, S and
                McKenney, A and Sorensen, D},
      TITLE = {{LAPACK} Users' Guide},
      EDITION = {Third},
      PUBLISHER = {Society for Industrial and Applied Mathematics},
      YEAR = 1999,
      ADDRESS = {Philadelphia, PA},
      ISBN = {0-89871-447-8 (paperback)} }

Fox-Li matrix has interesting pseudospectra (spiraling eigenvalues)
@article{fox1961resonant,
  title={Resonant modes in a maser interferometer},
  author={Fox, Arthur G and Li, Tingye},
  journal={Bell System Technical Journal},
  volume={40},
  number={2},
  pages={453--488},
  year={1961},
  publisher={Wiley Online Library}
}

LAPACK bounds on nonsymmetric eigenproblem condition number (STRSNA, STRSEN)
@article{bai1989conditioning,
  title={On the conditioning of the nonsymmetric eigenproblem: Theory and software},
  author={Bai, Z and Demmel, James and McKenney, A},
  year={1989},
  publisher={University of Tennessee}
}

Algorithm for 1-norm pseudospectra
@article{higham2000block,
  title={A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra},
    author={Higham, Nicholas J and Tisseur, Fran{\c{c}}oise},
      journal={SIAM Journal on Matrix Analysis and Applications},
        volume={21},
          number={4},
            pages={1185--1201},
              year={2000},
                publisher={SIAM}
                }

@article{van2015blis,
  title={{BLIS}: A framework for rapidly instantiating {BLAS} functionality},
    author={Van Zee, Field G and Van De Geijn, Robert A},
      journal={ACM Transactions on Mathematical Software},
        volume={41},
          number={3},
            pages={14},
              year={2015},
                publisher={ACM}
                }

@book{henry1994shifted,
  title={The shifted {Hessenberg} system solve computation},
    author={Henry, Greg},
      year={1994},
        publisher={Citeseer}
        }

@article{bischof1996parallel,
  title={A parallel algorithm for the {Sylvester} observer equation},
    author={Bischof, Christian H and Datta, Biswa Nath and Purkayastha, Avijit},
      journal={SIAM Journal on Scientific Computing},
        volume={17},
          number={3},
            pages={686--698},
              year={1996},
                publisher={SIAM}
                }