Bibliography

1

M. Brezina, P. Vanek, A Black-Box Iterative Solver Based on a Two-Level Schwarz Method, Computing, 63, 1999, 233-263.

2

W. L. Briggs, V. E. Henson, S. F.  McCormick, A Multigrid Tutorial, Second Edition, SIAM, 2000.

3

A. Buttari, P. D'Ambra, D. di Serafino, S. Filippone, Extending PSBLAS to Build Parallel Schwarz Preconditioners, 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.

4

A. Buttari, P. D'Ambra, D. di Serafino, S. Filippone, 2LEV-D2P4: a package of high-performance preconditioners for scientific and engineering applications, Applicable Algebra in Engineering, Communications and Computing, 18 (3) 2007, 223-239.

5

P. D'Ambra, S. Filippone, D. di Serafino, On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners, Applied Numerical Mathematics, Elsevier Science, 57 (11-12), 2007, 1181-1196.

6

X. C. Cai, M. Sarkis, A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems, SIAM Journal on Scientific Computing, 21 (2), 1999, 792-797.

7

X. C. Cai, O. B. Widlund, Domain Decomposition Algorithms for Indefinite Elliptic Problems, SIAM Journal on Scientific and Statistical Computing, 13 (1), 1992, 243-258.

8

T. Chan and T. Mathew, Domain Decomposition Algorithms, in A. Iserles, editor, Acta Numerica 1994, 61-143. Cambridge University Press.

9

P. D'Ambra, D. di Serafino, S. Filippone, MLD2P4: a Package of Parallel Multilevel Algebraic Domain Decomposition Preconditioners in Fortran 95, ACM Trans. Math. Softw., 37(3), 2010, art. 30.

10

T.A. Davis, Algorithm 832: UMFPACK - an Unsymmetric-pattern Multifrontal Method with a Column Pre-ordering Strategy, ACM Transactions on Mathematical Software, 30, 2004, 196-199. (See also http://www.cise.ufl.edu/ davis/)

11

P.R. Amestoy, C. Ashcraft, O. Boiteau, A. Buttari, J. L'Excellent, C. Weisbecker Improving multifrontal methods by means of block low-rank representations, SIAM Journal on Scientific Computing, volume 37 (3), 2015, A1452-A1474. See also http://mumps.enseeiht.fr.

12

J.W. Demmel, S.C. Eisenstat, J.R. Gilbert, X.S. Li and J.W.H. Liu, A supernodal approach to sparse partial pivoting, SIAM Journal on Matrix Analysis and Applications, 20 (3), 1999, 720-755.

13

J. J. Dongarra, J. Du Croz, I. S. Duff, S. Hammarling, A set of Level 3 Basic Linear Algebra Subprograms, ACM Transactions on Mathematical Software, 16 (1) 1990, 1-17.

14

J. J. Dongarra, J. Du Croz, S. Hammarling, R. J. Hanson, An extended set of FORTRAN Basic Linear Algebra Subprograms, ACM Transactions on Mathematical Software, 14 (1) 1988, 1-17.

15

J. J. Dongarra and R. C. Whaley, A User's Guide to the BLACS v. 1.1, Lapack Working Note 94, Tech. Rep. UT-CS-95-281, University of Tennessee, March 1995 (updated May 1997).

16

E. Efstathiou, J. G. Gander, Why Restricted Additive Schwarz Converges Faster than Additive Schwarz, BIT Numerical Mathematics, 43 (5), 2003, 945-959.

17

S. Filippone, A. Buttari, PSBLAS-3.0 User's Guide. A Reference Guide for the Parallel Sparse BLAS Library, 2012, available from http://www.ce.uniroma2.it/psblas/.

18

Salvatore Filippone and Alfredo Buttari. Object-Oriented Techniques for Sparse Matrix Computations in Fortran 2003. ACM Transactions on on Mathematical Software, 38 (4), 2012, art. 23.

19

S. Filippone, M. Colajanni, PSBLAS: A Library for Parallel Linear Algebra Computation on Sparse Matrices, ACM Transactions on Mathematical Software, 26 (4), 2000, 527-550.

20

W. Gropp, S. Huss-Lederman, A. Lumsdaine, E. Lusk, B. Nitzberg, W. Saphir, M. Snir, MPI: The Complete Reference. Volume 2 - The MPI-2 Extensions, MIT Press, 1998.

21

C. L. Lawson, R. J. Hanson, D. Kincaid, F. T. Krogh, Basic Linear Algebra Subprograms for FORTRAN usage, ACM Transactions on Mathematical Software, 5 (3), 1979, 308-323.

22

X. S. Li, J. W. Demmel, SuperLU_DIST: A Scalable Distributed-memory Sparse Direct Solver for Unsymmetric Linear Systems, ACM Transactions on Mathematical Software, 29 (2), 2003, 110-140.

23

Y. Notay, P. S. Vassilevski, Recursive Krylov-based multigrid cycles, Numerical Linear Algebra with Applications, 15 (5), 2008, 473-487.

24

Y. Saad, Iterative methods for sparse linear systems, 2nd edition, SIAM, 2003.

25

B. Smith, P. Bjorstad, W. Gropp, Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press, 1996.

26

M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra, MPI: The Complete Reference. Volume 1 - The MPI Core, second edition, MIT Press, 1998.

27

K. Stüben, An Introduction to Algebraic Multigrid, in A. Schüller, U. Trottenberg, C. Oosterlee, Multigrid, Academic Press, 2001.

28

R. S. Tuminaro, C. Tong, Parallel Smoothed Aggregation Multigrid: Aggregation Strategies on Massively Parallel Machines, in J. Donnelley, editor, Proceedings of SuperComputing 2000, Dallas, 2000.

29

P. Vanek, J. Mandel and M. Brezina, Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems, Computing, 56 (3) 1996, 179-196.