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E. Timsit, L. Grigori, and O. Balabanov, Randomized
Orthogonal Projection Methods for Krylov Subspace Solvers,
pdf, Feb 2023.
V. Bharadwaj et al, Fast Exact Leverage Score Sampling from
Khatri-Rao Products with Applications to Tensor Decomposition ,
pdf, Jan 2023.
R. Murray et al, Randomized Numerical Linear Algebra: A
Perspective on the Field with an Eye to Software, pdf,
S. Badreddine, I. Chollet, L. Grigori, Factorized structure of
the long-range two-electron integrals tensor and its application in
pdf, Oct 2022.
O. Balabanov, M. Beaupère, L. Grigori and V. Lederer, Block
subsampled randomized Hadamard transform for low-rank approximation
on distributed architectures, pdf, Oct 2022.
H. Al Daas, G. Ballard, L. Grigori, S. Kumar, K. Rouse,
Communication Lower Bounds and Optimal Algorithms for Multiple
Tensor-Times-Matrix Computation, pdf, July 2022.
O. Balabanov and L. Grigori,
Randomized block Gram-Schmidt process for solution of linear
systems and eigenvalue problems, pdf, November 2021.
M. Beaupere and L. Grigori,
Communication avoiding low rank approximation based on QR with
tournament pivoting, pdf, 2020.
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52. L. Grigori, S.A. Hirstoaga, J. Salomon, A Parareal algorithm for a highly oscillating
Vlasov-Poisson system with reduced models for the coarse solving,
Computers and Mathematics with Applications, in press, 2022.
51. V.-T. Nguyen and L. Grigori, Interpretation of parareal as a two-level additive Schwarz in time preconditioner and its acceleration with GMRES,
Numerical Algorithms Journal, 10.1007/s11075-022-01492-8, 2023.
50. M. Beaupère, D. Frenkiel, L. Grigori,
Higher-order QR with tournament pivoting for tensor compression,
pdf, 2022, in press,
SIAM Journal on Matrix Analysis and Applications.
49.J. Demmel, L. Grigori, and A. Rusciano,
An improved analysis and unified perspective on deterministic
and randomized low rank matrix approximations, pdf, in press, 2022, SIAM
Journal on Matrix Analysis and Applications.
48. I. Chollet, X. Claeys, P. Fortin, and L. Grigori, A Directional Equispaced interpolation-based Fast Multipole Method
for oscillatory kernels,
Journal on Scientific Computing, in press, 2022.
47. H. El Bouhargani, A. Jamal, D. Beck, J. Errard, L. Grigori, and
R. Stompor, MAPPRAISER: A massively parallel map-making framework
for multi-kilo pixel CMB experiments, pdf,
Astronomy and Computing, 2022.
46. O. Balabanov and L. Grigori,
Randomized Gram-Schmidt process with application to
GMRES, pdf , SIAM
Journal on Scientific Computing, 44 (3), A1450-A1474, 2022. Available
on arxiv since 2020. Matlab
code by O. Balabanov available here.
45. L. Grigori, S. Hirstoaga, J. Salomon, V.T. Nguyen,
Reduced model-based parareal simulations
of oscillatory singularly perturbed ordinary differential
equations, pdf, Journal
of Computational Physics, Vol 436, 2021.
44. H. Al Daas, L. Grigori, P. Jolivet, P. H. Tournier,
A multilevel Schwarz preconditioner based on a hierarchy of robust coarse spaces,
pdf, code for reproducing the results available
in HPDDM by P. Jolivet
and available through Petsc PCHPDDM,
SIAM Journal on
Scientific Computing, Vol 43(3), pages 1907 - 1923, 2021.
43. S. Das, J. Demmel, K. Fountoulakis, L. Grigori, M. W. Mahoney,
Parallel and Communication Avoiding Least Angle Regression
pdf, SIAM Journal
on Scientific Computing, Vol 43(2), pages 154--176, 2021.
42. H. Al Daas, L. Grigori, P. Henon, P. Ricoux,
Recycling Krylov subspaces and
reducing deflation subspaces for solving sequence of linear systems, in revision,
ACM Transactions on Mathematical Software, Vol 47(2), pages 1--30. 2021,
INRIA TR 9206.
41. V. Ehrlacher, L. Grigori, D. Lombardi, H. Song,
Adaptive hierarchical subtensor partitioning for tensor
compression, pdf, SIAM Journal
on Scientific Computing, Vol 43(3), pages 139--163, 2021.
40. A. Anciaux-Sedrakian, L. Grigori, Z. Jorti and S. Yousef,
An a posteriori-based adaptive preconditioner for
controlling a local algebraic error norm, Bit numerical
mathematics, pdf, 61(1), 209-235, 2020.
39. A. Anciaux-Sedrakian, L. Grigori, Z. Jorti and S. Yousef,
Adaptive linear solution process for single-phase Darcy flow,
OGST, Oil & Gas Science and Technology, 2020.
38. J. Papez, L. Grigori, and R. Stompor,
Accelerating linear system solvers for time domain component separation of cosmic microwave background data,
pdf , Astronomy and Astrophysics Journal, 638, A73, 16 pages, 2020.
37. J. Dongarra, L. Grigori, N.J. Higham
Numerical algorithms for high-performance computational
science, Philosophical Transactions of the Royal Society A, Vol. 378, No. 2166 (not refereed), 2020,
36. A. Ayala, X. Claeys, L. Grigori,
Linear-time CUR approximation of BEM matrices ,
Journal of Computational and Applied Mathematics, Vol 368, 2020.
35. A. Anciaux-Sedrakian, L. Grigori, Z. Jorti, J. Papez,
Adaptive resolution of linear systems based on a
posteriori error estimators, pdf, Numerical Algorithms, 84:331-364, 2020.
34. L. Grigori, O. Tissot
Scalable linear solvers based on enlarged Krylov subspaces
with dynamic reduction of search directions, SIAM
Journal on Scientific Computing, 41(5), C522–C547, 2019, pdf.
33. L. Grigori, Q. Niu, Y. Xu,
Stabilized Dimensional Factorization Preconditioner for Solving Incompressible
Navier-Stokes Equations, Applied Numerical Mathematics, Vol. 146,
pages 309-327, 2019.
32. A. Ayala, X. Claeys, and L. Grigori,
ALORA: Affine Low-Rank Approximations , Journal of Scientific Computing,
Vol 79, Issue 2, May 2019, Pages 1135-1160, 2019,
also available as Tech Report 9170, pdf .
31. H. Al Daas, L. Grigori
A class of efficient locally constructed preconditioners based on coarse spaces ,
SIAM J. Matrix Anal. & Appl.,
doi, 40, pp. 66-91, 2019, pdf .
30. J. Papez, L. Grigori, and R. Stompor,
Solving linear equations with messenger-field and conjugate gradients techniques - an
application to CMB data analysis, Astronomy and Astrophysics Journal, Section Numerical methods and codes, Vol 620, A59,
pdf , 2018.
29. H. Al Daas, L. Grigori, P. Henon, and P. Ricoux,
Enlarged GMRES for solving linear systems with one or multiple right-hand sides, IMA Journal of Numerical Analysis,
28. L. Grigori, F. Nataf, S. Yousef, S. Donfack, R. Lacroix,
Robust algebraic Schur complement preconditioners based on low rank corrections ,
in submission, 2017,
preliminary version published as
INRIA TR 8557 .
27. L. Grigori, S. Cayrols, and J. Demmel,
Low rank approximation of a sparse matrix based on LU factorization with column and row tournament pivoting, SIAM Journal on Scientific Computing, Vol. 40, No. 2, C181-C209, 2018, pdf.
26. L. Grigori,
Introduction to Communication Avoiding Algorithms for Direct Methods of Factorization in
Linear Algebra, Chapter in Computational Mathematics, Numerical Analysis and Applications, SEMA SIMAI Springer Series, Lecture Notes of the XVII 'Jacques-Louis Lions' Spanish-French School, 2017.
25. A. Azad, G. Ballard, A. Buluc, J. Demmel, L. Grigori, O. Schwartz, S. Toledo, S. Williams
Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication,
SIAM Journal on Scientific Computing, Vol. 38, No. 6, pp. C624-C651, 2016, pdf, and on arxiv .
24. A. Anciaux-Sedrakian, L. Grigori, S. Moufawad, S. Yousef,
S-step BiCGStab Algorithms for Geoscience Dynamic
Oil and Gas Science and Technology, Rev. IFP Energies nouvelles, 2016.
23. L. Grigori, S. Moufawad, F. Nataf
Enlarged Krylov Subspace Conjugate Gradient Methods for
Reducing Communication , pdf,
SIAM J. Matrix Anal. & Appl, 2016.
22. G. Ballard, J. Demmel, L. Grigori, M. Jacquelin,
N. Knight, D. Nguyen
vectors for QR factorization ,
Journal of Parallel and Distributed Computing, Aug 2015, available here.
21. L. Grigori, S. Moufawad,
Communication avoiding ILU0 preconditioner , pdf
SIAM Journal on Scientific Computing, 2015, Vol. 37, Issue 2.
20. J. Demmel, L. Grigori, M. Gu, and H. Xiang
Communication avoiding rank revealing QR factorization with column pivoting, pdf,
SIAM J. Matrix Anal. & Appl, Vol. 36, No. 1, pp. 55-89, 2015.
19. M. Szydlarski, L. Grigori, and R. Stompor,
Accelerating the Cosmic Microwave Background map-making
problem through preconditioning,
Astronomy and Astrophysics Journal, Section Numerical methods and
codes, Volume 572, Article A39, 18 pages,
pdf , December 2014.
18. L. Grigori, F. Nataf, and L. Qu
Overlapping for Preconditioners based on Incomplete Factorizations and Nested Dissection,
Numerical Linear Algebra with Applications Journal, Volume 22, Issue 1, Pages 48-75, 2015.
17. R. Fezzani, L. Grigori, F. Nataf, and K. Wang
Block filtering decomposition , Numerical Linear
Algebra with Applications Journal, Volume 21, Issue 6, pages 703 - 721, 2014, preliminary version
published as INRIA TR
16. M. Szydlarski, P. Esterie, J. Falcou, L. Grigori, and R. Stompor,
Spherical harmonic transform on heterogeneous
architectures using hybrid programming ,
Concurrency and Computation: Practice and Experience Journal, Vol. 26, Issue 3, Pages 683-711, 2014, preliminary version published as
15. A. Khabou, J. Demmel, L. Grigori, and M. Gu
LU factorization with panel rank revealing pivoting and
its communication avoiding version,
SIAM J. Matrix Anal. & Appl., Vol. 34, No. 3, pages 1401-1429, 2013, preliminary version published as LAWN 263, pdf.
14. J. Demmel, L. Grigori, M. F. Hoemmen, and J. Langou,
Communication-optimal parallel and sequential QR and LU factorizations,
SIAM Journal on Scientific Computing, Vol. 34, No 1, 2012,
[pdf] (also available on arXiv:0808.2664v1), short version of
UCB-EECS-2008-89 and LAWN 204, available since 2008,
SIAM Siag on Supercomputing Best Paper Prize, 2016.
13. L. Grigori, J. Demmel, and H. Xiang,
CALU: a communication optimal LU factorization
SIAM J. Matrix Anal. & Appl., 32, pp. 1317-1350, 2011,
preliminary version published as LAWN 226
12. L. Grigori, F. Nataf, and Q. Niu,
Two sides tangential filtering decomposition,
Journal of Computational and Applied Mathematics, Vol. 235,
pages 2647-2661, 2010, preliminary version as INRIA TR 6554
11. L. Grigori, E. Boman, S. Donfack, and T. Davis,
Hypergraph-based unsymmetric nested dissection ordering
for sparse LU factorization,
SIAM Journal on Scientific Computing, Vol. 32, No. 6,
2010, [pdf] , preliminary version as INRIA TR 6520
10. L. Grigori, D. Nuentsa Wakam, and H. Xiang
Saving flops in LU based shift-and-invert strategy,
Journal of Computational and Applied Mathematics, Vol. 234,
Issue 12, Pages 3216-3225, 2010.
9. M. Becka, G. Oksa, M. Vajtersic, and L. Grigori,
On iterative QR pre-processing in the parallel block-Jacobi SVD algorithm ,
Parallel Computing Journal, Vol. 36, Issues 5-6, pages 297-307, 2010.
8. Q. Niu, L. Grigori, P. Kumar, and F. Nataf,
Modified tangential frequency filtering decomposition and its Fourier analysis,
Numerische Mathematik, Vol. 116, No. 1, pages 123-148, 2010, preliminary version published as INRIA TR 6662
7. H. Xiang and L. Grigori,
approximation preconditioners for convection-diffusion model
Numerical Linear Algebra with Applications
Journal, Volume 17 Issue 4, Pages 691 - 712, 2009. (Preliminary version published as INRIA TR
6. L. Grigori, J. R. Gilbert, and M. Cosnard,
Structure Prediction for Sparse Gaussian Elimination with Partial Pivoting.
SIAM Journal on Matrix Analysis and its Applications, Vol. 30, Issue 4, pp 1520-1545, 2008 [pdf] .
5. G.-A. Atenekeng, L. Grigori, and M. Sosonkina,
A Partitioning Algorithm for Block-Diagonal Matrices with Overlap,
Parallel Computing, vol. 34, no 6, pp 332-344, 2008
4. L. Grigori, J. W. Demmel, and X.S. Li,
Parallel Symbolic Factorization for Sparse LU Factorization with Static Pivoting
SIAM Journal on Scientific Computing, Volume 29 Issue 3, Pages 1289-1314, 2007.
pdf , DOI: 10.1137/050638102.
3. L. Grigori, M. Cosnard, and E. Ng,
On the Row Merge Tree for Sparse LU Factorization with Partial Pivoting,
BIT Numerical Mathematics Journal, Volume 47, Number 1, 2007, Pages 45-76, 2007.
pdf , DOI 10.1007/s10543-007-0116-1.
2. L. Grigori and X.S. Li,
Towards an Accurate Performance Modeling of Parallel Sparse LU Factorization,
Applicable Algebra in Engineering, Communication, and Computing Journal, special issue on Computational Linear Algebra and Sparse Matrix Computation, Springer-Verlag, Number 18, Issue 3, 2007.
pdf , DOI 10.1007/s00200-007-0036-y.
1. J. Gilbert and L. Grigori,
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A Note on the Column Elimination Tree,
SIAM Journal on Matrix Analysis and its Applications. Volume 25, Number 1 (pp 143-151), 2003.
Special Issue and other publications
Lessons learned from urgent computing in Europe: Tackling
the COVID-19 pandemic,
N. Lopez, L. Del Debbio, M. Baaden, M. Praprotnik, L. Grigori,
et al, PNAS (refereed), 2021, 118 (46), online.
Guest editor of a volume of Philosophical Transactions of
the Royal Society A. Discussion meeting issue ‘Numerical algorithms for
high-performance computational science’ organised and edited
with J. Dongarra and N. J. Higham.
Vol. 378, No. 2166, (March 2020) available online.
Guest Editor in Charge
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Special Issue of Parallel Computing Journal (Elsevier) on
Parallel Matrix Algorithms and Applications, Vol. 34, Nos. 6
- 8, June 2008.
Conference proceedings (selected)
22. H. Al Daas, G. Ballard, L. Grigori, S. Kumar, and
K. Rouse, Parallel Memory-Independent Communication Bounds
for SYRK, ACM SPAA, Symposium on Parallel Algorithms and Applications, 2023.
21. H. Al Daas, G. Ballard, L. Grigori, S. Kumar, and
K. Rouse, Tight Memory-Independent Parallel Matrix
Multiplication Communication Lower Bounds , brief announcement,
ACM SPAA, Symposium on Parallel Algorithms and Applications, 2022,
20. G. Ballard, J. Demmel, L. Grigori, M. Jacquelin and N. Knight,
A 3D Parallel Algorithm for QR Decomposition,
Proceedings of ACM SPAA, Symposium on Parallel Algorithms and
19. E. Carson, J. Demmel, L. Grigori, N. Knight, P. Koanantakool, O. Schwartz and H. V. Simhadri,
Write-Avoiding Algorithms, Proceedings of IEEE
International Parallel & Distributed Processing Symposium,
IPDPS 2016, shorter version of Technical Report UCB/EECS-2015-163 , June 2015, 47 pages.
18. L. Grigori, M. Jacquelin, and A. Khabou
Performance predictions of multilevel communication optimal LU and
QR factorizations on hierarchical platforms,
International Supercomputing Conference 2014, LNCS.
17. G. Ballard, J. Demmel, L. Grigori, M. Jacquelin, H. D. Nguyen and E. Solomonik
Reconstructing Householder Vectors from Tall-Skinny QR ,
Proceedings of IEEE
International Parallel & Distributed Processing Symposium,
IPDPS 2014. pdf.
16. L. Qu, L. Grigori, and F. Nataf,
Parallel design and performance of nested filtering factorization preconditioner,
Proceedings of the IEEE/ACM SuperComputing SC13 Conference, November 2013. Best student paper finalist .
15. G. Ballard, A. Buluc, J. Demmel, L. Grigori, B. Lipshitz, O. Schwartz and S. Toledo,
Communication Optimal Parallel Multiplication of Sparse Random Matrices,
Proceedings of ACM Symposium on Parallelism in Algorithms and Architectures SPAA 2013 Conference,
14. L. Grigori, R. Stompor, and M. Szydlarski
A parallel two-level preconditioner for Cosmic Microwave
Background map-making , Proceedings of the IEEE/ACM
SuperComputing SC12 Conference, November 2012.
13. S. Donfack, L. Grigori, A. Khabou,
Communication avoiding through a multilevel LU factorization ,
Proceedings of Euro-Par 2012.
12. G. Fabbian, M. Szydlarski, R. Stompor, L. Grigori, and
Spherical harmonic transforms with
S2HAT, proceedings of the Astronomical Data Analysis
Software and Systems (ADASS XXI) conference, Nov, 5-10,
2011, Eds. P. Ballester and D. Egret, to apear in ASP
Conference Series, 2012.
11. M. Baboulin, S. Donfack, J. Dongarra, L. Grigori,
A. Remy, S. Tomov,
A class of communication-avoiding algorithms for solving general dense
linear systems on CPU/GPU parallel machines ,
Proceedings of International Conference on Computational
Science ICCS 2012.
10. S. Donfack, L. Grigori, W. Gropp, and V. Kale,
Hybrid static/dynamic scheduling for already optimized
dense matrix factorization , Proceedings of IEEE
International Parallel & Distributed Processing Symposium
IPDPS, 2012, preliminary version published as
9. I. O. Hupca, J. Falcou, L. Grigori, and R. Stompor,
Spherical Harmonic Transform with GPUs ,
Workshop on High Performance Scientific Software, HPSS 2011,
INRIA TR 7409 .
8. L. Grigori, P.-Y. David, J. Demmel, and S. Peyronnet,
Brief announcement: Lower bounds on communication for sparse
Cholesky factorization of a model problem ,
(3 pages) ACM SPAA 2010, pdf.
7. S. Donfack, L. Grigori, and A. Kumar Gupta,
Adapting communication-avoiding LU and QR
factorizations to multicore architectures,
Proceedings of IEEE International Parallel & Distributed
Processing Symposium IPDPS, April 2010.
6. L. Grigori, J. Demmel, and H. Xiang,
Communication avoiding Gaussian elimination,
Proceedings of the IEEE/ACM SuperComputing SC08 Conference, November 2008. Also INRIA TR 6523 pdf
5. X S Li, J Demmel, L Grigori, M Gu, J Xia, S Jardin, C Sovinec,
and L-Q Lee
Enhancing scalability of sparse direct methods,
Journal of Physics : Conference Series, Volume 78, 2007.
4. L. Grigori and X.S. Li,
Performance Analysis of Parallel Right-Looking Sparse
LU Factorization on Two Dimensional Grid of Processors,
PARA'04 Workshop on State-of-the-art in Scientific Computing, June 20-23 2004, Copenhagen, Denmark, pp 768-777, LNCS 3732, Springer, 2006.
3. L. Grigori and X.S. Li,
A New Scheduling Algorithm for Parallel Sparse LU
Factorization with Static Pivoting,
Proceedings of the IEEE/ACM SuperComputing SC2002 Conference, November 2002. ps
2. M. Cosnard and L. Grigori,
A Parallel Algorithm for Sparse Symbolic LU
Factorization without Pivoting on Out of Core Matrices,
ACM International Conference on
Supercomputing, June 2001, Sorrento, Italy. ps
1. M. Cosnard and L. Grigori,
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Using Postordering and Static Symbolic Factorization
for Parallel Sparse LU ,
IEEE International Parallel and Distributed Processing Symposium
(IPDPS'2000), Cancun, Mexico.
Tech reports (not published elsewhere)
L. Grigori, O. Tissot
Reducing the communication and computational costs of Enlarged Krylov subspaces Conjugate Gradient,
INRIA TR 9023 , 2017.
S. Becker, J. Folberth, L. Grigori
URV Factorization with Random Orthogonal System Mixing,
pdf , 2017.
P. Cargemel, L. Grigori, and R. Stompor,
Communication in the CMB map-making problem.
M. Sharify, S. Gaubert, and L. Grigori,
A parallel preprocessing for the optimal assignment
problem based on diagonal scaling,
L. Grigori, P. Kumar, F. Nataf, and K. Wang,
A class of multilevel parallel preconditioning
INRIA TR 7410 .
P. Kumar, L. Grigori, F. Nataf, and Q. Niu,
Combinative preconditioning based on Relaxed Nested Factorization and Tangential Filtering preconditioner ,
preliminary version as INRIA TR 6955
J. Demmel, L. Grigori, M. F. Hoemmen, and J. Langou,
> Top of the page
Communication-optimal parallel and sequential QR and LU factorizations : Theory and Practice,
204 (long technical report not submitted elsewhere)