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Bibliography< / A >
< / H2 > < DL COMPACT > < DD >
< P >
< P > < / P > < DT > < A NAME = "MUMPS" > 1< / A >
< DD >
P. R. Amestoy, C. Ashcraft, O. Boiteau, A. Buttari, J. L'Excellent, C. Weisbecker,
< EM > Improving multifrontal methods by means of block low-rank representations< / EM > ,
SIAM Journal on Scientific Computing, volume 37 (3), 2015, A1452-A1474.
See also < TT > http://mumps.enseeiht.fr< / TT > .< P > < / P > < DT > < A NAME = "BREZINA_VANEK" > 2< / A >
< DD >
M. Brezina, P. Vanek,
< EM > A Black-Box Iterative Solver Based on a Two-Level Schwarz Method< / EM > ,
Computing, 63, 1999, 233-263.< P > < / P > < DT > < A NAME = "Briggs2000" > 3< / A >
< DD >
W. L. Briggs, V. E. Henson, S. F. McCormick,
< EM > A Multigrid Tutorial, Second Edition< / EM > ,
SIAM, 2000.< P > < / P > < DT > < A NAME = "para_04" > 4< / A >
< DD >
A. Buttari, P. D'Ambra, D. di Serafino, S. Filippone,
< EM > Extending PSBLAS to Build Parallel Schwarz Preconditioners< / EM > ,
in J. Dongarra, K. Madsen, J. Wasniewski, editors,
Proceedings of PARA 04 Workshop on State of the Art
in Scientific Computing, Lecture Notes in Computer Science,
Springer, 2005, 593-602.< P > < / P > < DT > < A NAME = "aaecc_07" > 5< / A >
< DD >
A. Buttari, P. D'Ambra, D. di Serafino, S. Filippone,
< EM > 2LEV-D2P4: a package of high-performance preconditioners
for scientific and engineering applications< / EM > ,
Applicable Algebra in Engineering, Communications and Computing,
18 (3) 2007, 223-239.< P > < / P > < DT > < A NAME = "CAI_SARKIS" > 6< / A >
< DD >
X. C. Cai, M. Sarkis,
< EM > A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems< / EM > ,
SIAM Journal on Scientific Computing, 21 (2), 1999, 792-797.< P > < / P > < DT > < A NAME = "apnum_07" > 7< / A >
< DD >
P. D'Ambra, S. Filippone, D. di Serafino,
< EM > On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners< / EM > ,
Applied Numerical Mathematics, Elsevier Science,
57 (11-12), 2007, 1181-1196.< P > < / P > < DT > < A NAME = "MLD2P4_TOMS" > 8< / A >
< DD >
P. D'Ambra, D. di Serafino, S. Filippone,
< I > MLD2P4: a Package of Parallel Multilevel
Algebraic Domain Decomposition Preconditioners
in Fortran 95< / I > , ACM Trans. Math. Softw., 37(3), 2010, art. 30.< P > < / P > < DT > < A NAME = "UMFPACK" > 9< / A >
< DD >
T. A. Davis,
< EM > Algorithm 832: UMFPACK - an Unsymmetric-pattern Multifrontal
Method with a Column Pre-ordering Strategy< / EM > ,
ACM Transactions on Mathematical Software, 30, 2004, 196-199.
(See also < TT > http://www.cise.ufl.edu/~davis/< / TT > )< P > < / P > < DT > < A NAME = "SUPERLU" > 10< / A >
< DD >
J. W. Demmel, S. C. Eisenstat, J. R. Gilbert, X. S. Li, J. W. H. Liu,
< EM > A supernodal approach to sparse partial pivoting< / EM > ,
SIAM Journal on Matrix Analysis and Applications, 20 (3), 1999, 720-755.< P > < / P > < DT > < A NAME = "blas3" > 11< / A >
< DD >
J. J. Dongarra, J. Du Croz, I. S. Duff, S. Hammarling,
< I > A set of Level 3 Basic Linear Algebra Subprograms< / I > ,
ACM Transactions on Mathematical Software, 16 (1) 1990, 1-17.< P > < / P > < DT > < A NAME = "blas2" > 12< / A >
< DD >
J. J. Dongarra, J. Du Croz, S. Hammarling, R. J. Hanson,
< I > An extended set of FORTRAN Basic Linear Algebra Subprograms< / I > ,
ACM Transactions on Mathematical Software, 14 (1) 1988, 1-17.< P > < / P > < DT > < A NAME = "PSBLASGUIDE" > 13< / A >
< DD >
S. Filippone, A. Buttari,
< EM > PSBLAS 3.5.0 User's Guide. A Reference Guide for the Parallel Sparse BLAS Library< / EM > , 2012,
available from < TT > https://github.com/sfilippone/psblas3/tree/master/docs< / TT > .< P > < / P > < DT > < A NAME = "PSBLAS3" > 14< / A >
< DD >
S. Filippone, A. Buttari,
< EM > Object-Oriented Techniques for Sparse Matrix Computations in Fortran 2003< / EM > .
ACM Transactions on on Mathematical Software, 38 (4), 2012, art. 23.< P > < / P > < DT > < A NAME = "psblas_00" > 15< / A >
< DD >
S. Filippone, M. Colajanni,
< EM > PSBLAS: A Library for Parallel Linear Algebra
Computation on Sparse Matrices< / EM > ,
ACM Transactions on Mathematical Software, 26 (4), 2000, 527-550.< P > < / P > < DT > < A NAME = "MPI2" > 16< / A >
< DD >
W. Gropp, S. Huss-Lederman, A. Lumsdaine, E. Lusk, B. Nitzberg, W. Saphir, M. Snir,
< EM > MPI: The Complete Reference. Volume 2 - The MPI-2 Extensions< / EM > ,
MIT Press, 1998.< P > < / P > < DT > < A NAME = "blas1" > 17< / A >
< DD >
C. L. Lawson, R. J. Hanson, D. Kincaid, F. T. Krogh,
< I > Basic Linear Algebra Subprograms for FORTRAN usage< / I > ,
ACM Transactions on Mathematical Software, 5 (3), 1979, 308-323.< P > < / P > < DT > < A NAME = "SUPERLUDIST" > 18< / A >
< DD >
X. S. Li, J. W. Demmel,
< EM > SuperLU_DIST: A Scalable Distributed-memory
Sparse Direct Solver for Unsymmetric Linear Systems< / EM > ,
ACM Transactions on Mathematical Software, 29 (2), 2003, 110-140.< P > < / P > < DT > < A NAME = "Notay2008" > 19< / A >
< DD >
Y. Notay, P. S. Vassilevski,
< EM > Recursive Krylov-based multigrid cycles< / EM > ,
Numerical Linear Algebra with Applications, 15 (5), 2008, 473-487. < P > < / P > < DT > < A NAME = "Saad_book" > 20< / A >
< DD >
Y. Saad,
< EM > Iterative methods for sparse linear systems< / EM > , 2nd edition, SIAM, 2003.< P > < / P > < DT > < A NAME = "dd2_96" > 21< / A >
< DD >
B. Smith, P. Bjorstad, W. Gropp,
< EM > Domain Decomposition: Parallel Multilevel Methods for Elliptic
Partial Differential Equations< / EM > ,
Cambridge University Press, 1996.< P > < / P > < DT > < A NAME = "MPI1" > 22< / A >
< DD >
M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra,
< EM > MPI: The Complete Reference. Volume 1 - The MPI Core< / EM > , second edition,
MIT Press, 1998.< P > < / P > < DT > < A NAME = "Stuben_01" > 23< / A >
< DD >
K. Stü ben,
< EM > An Introduction to Algebraic Multigrid< / EM > ,
in A. Schü ller, U. Trottenberg, C. Oosterlee, Multigrid,
Academic Press, 2001.< P > < / P > < DT > < A NAME = "TUMINARO_TONG" > 24< / A >
< DD >
R. S. Tuminaro, C. Tong,
< EM > Parallel Smoothed Aggregation Multigrid: Aggregation Strategies on Massively Parallel Machines< / EM > , in J. Donnelley, editor, Proceedings of SuperComputing 2000, Dallas, 2000.< P > < / P > < DT > < A NAME = "VANEK_MANDEL_BREZINA" > 25< / A >
< DD >
P. Vanek, J. Mandel, M. Brezina,
< EM > Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems< / EM > ,
Computing, 56 (3) 1996, 179-196.
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