[1]   A. Aprovitola, P. D’Ambra, F. Denaro, D. di Serafino, S. Filippone, Scalable algebraic multilevel preconditioners with application to CFD, in Proc. of CFD 2008, LNCSE, 74, (2010), 15–27.

[2]   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

[3]   D. Bertaccini and S. Filippone, Sparse approximate inverse preconditioners on high performance GPU platforms, Comput. Math. Appl., 71, (2016), no. 3, 693–711.

[4]   M. Brezina, P. Vaněk, A Black-Box Iterative Solver Based on a Two-Level Schwarz Method, Computing, 63, 1999, 233–263.

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

[6]   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.

[7]   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.

[8]   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.

[9]   U.. V. Catalyurek, F. Dobrian, A. Gebremedhin, M. Halappanavar, and A. Pothen, Distributed-memory parallel algorithms for matching and coloring, in PCO’11 New Trends in Parallel Computing and Optimization, IEEE International Symposium on Parallel and Distributed Processing Workshops, IEEE CS, 2011.

[10]   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.

[11]   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.

[12]   P. D’Ambra and P. S. Vassilevski, Adaptive AMG with coarsening based on compatible weighted matching, Computing and Visualization in Science, 16, (2013) 59–76.

[13]   P. D’Ambra, S. Filippone and P. S. Vassilevski, BootCMatch: a software package for bootstrap AMG based on graph weighted matching, ACM Transactions on Mathematical Software, 44, (2018) 39:1–39:25.

[14]   P. D’Ambra, F Durastante, S. Filippone, AMG preconditioners for Linear Solvers towards Extreme Scale, 2020, arXiv:2006.16147v3.

[15]   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

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

[17]   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.

[18]   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.

[19]   S. Filippone, P. D’Ambra, M. Colajanni, Using a Parallel Library of Sparse Linear Algebra in a Fluid Dynamics Application Code on Linux Clusters, in Proc. of ParCo 2001, Parallel Computing, Advances and Current Issues, 2002.

[20]   S. Filippone, A. Buttari, PSBLAS 3.5.0 User’s Guide. A Reference Guide for the Parallel Sparse BLAS Library, 2012, available from

[21]   S. Filippone, A. Buttari, Object-Oriented Techniques for Sparse Matrix Computations in Fortran 2003. ACM Transactions on on Mathematical Software, 38 (4), 2012, art. 23.

[22]   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.

[23]   S. Gratton, P. Henon, P. Jiranek and X. Vasseur, Reducing complexity of algebraic multigrid by aggregation, Numerical Lin. Algebra with Applications, 2016, 23:501-518

[24]   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.

[25]   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.

[26]   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.

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

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

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

[30]   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.

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

[32]   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.

[33]   P. Vaněk, J. Mandel, M. Brezina, Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems, Computing, 56 (3) 1996, 179–196.