@string{TOMS        = "{ACM} Trans. Math. Software"}
@string{SIMAX       = "{SIAM} J. Matrix Anal. Appl."}
@string{SIAMJSC     = "{SIAM} J. Sci. Comput."}

@article{Davis08a,
	author = {Davis, T. A.},
	title = {Multifrontal multithreaded rank-revealing sparse {QR} factorization},
	journal=TOMS,
	year = {2008},
        note = {under submission}
        }

@article{Davis08b,
	author = {Davis, T. A.},
	title = {Algorithm 8xx: {SuiteSparseQR}, a multifrontal multithreaded sparse QR factorization package},
	journal=TOMS,
	year = {2008},
        note = {under submission}
        }

@article{GilbertMolerSchreiber,
	author={Gilbert, J. R. and Moler, C. and Schreiber, R.},
	title={Sparse matrices in {MATLAB}:  design and implementation},
	journal=SIMAX,
	year={1992}
	,volume={13}
	,number={1}
	,pages={333-356}
}

@incollection{BoisvertPozoRemingtonBarrettDongarra97,
	author={Boisvert, R. F. and Pozo, R. and Remington, K. and Barrett, R. and Dongarra, J. J.},
	title={The {M}atrix {M}arket: A web resource for test matrix collections},
	booktitle={Quality of Numerical Software, Assessment and Enhancement},
	publisher={Chapman \& Hall},
	year={1997}
	,editor={Boisvert, R. F.}
	,pages={125-137}
	,address={London}
	,note={({\tt http://math.nist.gov/MatrixMarket})}
}

@article{AmestoyDavisDuff03,
	author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
	title={Algorithm 837: {AMD}, an approximate minimum degree ordering algorithm},
	journal=TOMS,
	year={2004}
	,volume={30}
	,number={3}
	,pages={381-388}}

@article{AmestoyDavisDuff96,
	author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
	title={An approximate minimum degree ordering algorithm},
	journal=SIMAX,
	year={1996}
	,volume={17}
	,number={4}
	,pages={886--905}
}

@Article{ChenDavisHagerRajamanickam09,
  author =       "Y. Chen and T. A. Davis and W. W. Hager and S. Rajamanickam",
  title =        "Algorithm 887: {CHOLMOD}, Supernodal Sparse {Cholesky} Factorization and Update/Downdate",
  journal =      TOMS,
  volume =       "35",
  year = {2009},
  number =       "3",
  accepted =     "26 March 2008",
  upcoming =     "true",
  abstract =     "CHOLMOD is a set of routines for factorizing sparse symmetric
positive definite matrices of the form $A$ or $AA^T$, updating/downdating a
sparse Cholesky factorization, solving linear systems, updating/downdating the
solution to the triangular system $Lx=b$, and many other sparse matrix
functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky
factorization relies on LAPACK and the Level-3 BLAS, and obtains a substantial
fraction of the peak performance of the BLAS.  Both real and complex matrices
are supported.  CHOLMOD is written in ANSI/ISO C, with both C and
MATLAB\texttrademark interfaces. It appears in MATLAB 7.2 as \verb'x=A\b' when
\verb'A' is sparse symmetric positive definite, as well as in several other
sparse matrix functions." }

@Article{DavisHager09,
  author =       "T. A. Davis and W. W. Hager",
  title =        "Dynamic Supernodes in Sparse {Cholesky} Update/downdate and Triangular Solves",
  journal =      TOMS,
  volume =       "35",
  year = {2009},
  number =       "4",
  accepted =     "2 May 2008",
  upcoming =     "true",
  abstract =     "The supernodal method for sparse Cholesky factorization
represents the factor $L$ as a set of supernodes, each consisting of a
contiguous set of columns of $L$ with identical nonzero pattern.  A
conventional supernode is stored as a dense submatrix.  While this is suitable
for sparse Cholesky factorization where the nonzero pattern of $L$ does not
change, it is not suitable for methods that modify a sparse Cholesky
factorization after a low-rank change to $A$ (an update/downdate, $\overline{A}
= A \pm WW^T$). Supernodes merge and split apart during an update/downdate.
Dynamic supernodes are introduced, which allow a sparse Cholesky
update/downdate to obtain performance competitive with conventional supernodal
methods.  A dynamic supernodal solver is shown to exceed the performance of the
conventional (BLAS-based) supernodal method for solving triangular systems.
These methods are incorporated into CHOLMOD, a sparse Cholesky factorization
and update/downdate package, which forms the basis of \verb'x=A\b' in MATLAB
when \verb'A' is sparse and symmetric positive definite." }

@article{DavisGilbertLarimoreNg00,
	author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.},
	title={A column approximate minimum degree ordering algorithm},
	journal=TOMS,
	year={2004}
	,volume={30}
	,number={3}
	,pages={353-376}}

@article{DavisGilbertLarimoreNg00_algo,
	author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.},
	title={Algorithm 836:  {COLAMD}, a column approximate minimum degree ordering algorithm},
	journal=TOMS,
	year={2004}
	,volume={30}
	,number={3}
	,pages={377-380}}

@article{dddh:90,
   author="J. J. Dongarra and J. J. {Du Croz} and Duff, I. S.  and S. Hammarling",
   year="1990",
   title="A set of {L}evel 3 {B}asic {L}inear {A}lgebra {S}ubprograms",
   journal=TOMS,
   volume ={16},
   pages  ={1--17}
}

@book{LAPACK,
     author={Anderson, E. and Bai, Z. and Bischof, C. H. and Blackford, S.
	and Demmel, J. W. and Dongarra, J. J. and {Du Croz}, J. and
	Greenbaum, A.  and Hammarling, S. and McKenney, A. and Sorensen, D. C.},
     title={{LAPACK} Users' Guide},
     publisher={SIAM},
     year=1999,
     address={Philadelphia},
     edition={3rd}
}

@Article{GotoVanDeGeijn08,
  author =       "K. Goto and R. van de Geijn",
  title =        "High Performance Implementation of the Level-3 {BLAS}",
  journal =      TOMS,
  volume =       "35",
  number =       "1",
  month =        jul,
  year =         "2008",
  pages =        "4",
  note =         "Article 4, 14 pages",
  URL =          "http://doi.acm.org/10.1145/1377603.1377607",
  abstract =     "A simple but highly effective approach for transforming
high-performance implementations on cache-based architectures of matrix-matrix
multiplication into implementations of other commonly used matrix-matrix
computations (the level-3 BLAS) is presented. Exceptional performance is
demonstrated on various architectures." }


@book{Reinders07,
     author={Reinders, J.},
     title={Intel Threading Building Blocks: Outfitting C++ for Multi-core Processor Parallelism},
     publisher={O'Reilly Media},
     address={Sebastopol, CA},
     year={2007}
}

@article{KarypisKumar98e,
	author={Karypis, G. and Kumar, V.},
	title={A fast and high quality multilevel scheme for partitioning irregular graphs},
	journal=SIAMJSC,
	year={1998}
	,volume={20}
	,pages={359-392}
	,annote={f. also TR-95-035, Dept. of Computer Science, Univ. of Minnesota, was KarypisKumar95a}
}
@article{10.1145/992200.992206,
author = {Davis, Timothy A.},
title = {Algorithm 832: UMFPACK V4.3---an Unsymmetric-Pattern Multifrontal Method},
year = {2004},
issue_date = {June 2004},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {30},
number = {2},
issn = {0098-3500},
url = {https://doi.org/10.1145/992200.992206},
doi = {10.1145/992200.992206},
abstract = {An ANSI C code for sparse LU factorization is presented that combines a column pre-ordering strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The pre-ordering and symbolic analysis phase computes an upper bound on fill-in, work, and memory usage during the subsequent numerical factorization. User-callable routines are provided for ordering and analyzing a sparse matrix, computing the numerical factorization, solving a system with the LU factors, transposing and permuting a sparse matrix, and converting between sparse matrix representations. The simple user interface shields the user from the details of the complex sparse factorization data structures by returning simple handles to opaque objects. Additional user-callable routines are provided for printing and extracting the contents of these opaque objects. An even simpler way to use the package is through its MATLAB interface. UMFPACK is incorporated as a built-in operator in MATLAB 6.5 as x = Ab when A is sparse and unsymmetric.},
journal = {ACM Trans. Math. Softw.},
month = {jun},
pages = {196–199},
numpages = {4},
keywords = {sparse nonsymmetric matrices, multifrontal method, linear equations, ordering methods}
}

  
