Literature

Publications (by the authors and other researchers) related to rank structured matrices. To suggest references to be included here, please email .

Keywords: fast, superfast, structure, direct, solver, rank, hierarchical, multipole, multifrontal, H-, H2-, HSS, Toeplitz, eigenvalue

  • 2016
    • Coulier, Pieter, Bryan Quaife, and Eric Darve. An efficient preconditioner for the fast simulation of a 2D Stokes flow in porous media. arXiv preprint arXiv:1609.04484 (2016).
    • J. Xia, Multi-layer hierarchical structures and factorizations, SIAM J. Matrix Anal. Appl., submitted, 2016, Purdue CCAM Report CCAM-2016-06. (PDF)
    • Yang, Kai, Hadi Pouransari, and Eric Darve. Sparse Hierarchical Solvers with Guaranteed Convergence. arXiv preprint arXiv:1611.03189 (2016).
    • X. Ye, J. Xia, R. Chan, S. Cauley, and V. Balakrishnan, A fast contour-integral eigensolver for non-Hermitian matrices, SIAM J. Matrix Anal. Appl.,submitted, 2016, Purdue CCAM Report CCAM-2016-04. (PDF)
    • Aminfar, Amirhossein, Sivaram Ambikasaran, and Eric Darve. A fast block low-rank dense solver with applications to finite-element matrices. Journal of Computational Physics 304 (2016): 170-188.
    • Aminfar, AmirHossein, and Eric Darve. A fast, memory efficient and robust sparse preconditioner based on a multifrontal approach with applications to finite-element matrices. International Journal for Numerical Methods in Engineering (2016).
    • Coulier, Pieter, and Eric Darve. Efficient mesh deformation based on radial basis function interpolation by means of the inverse fast multipole method. Computer Methods in Applied Mechanics and Engineering (2016).
    • X. Liu, J. Xia, and M. V. de Hoop, Parallel randomized and matrix-free direct solvers for large structured dense linear systems, SIAM J. Sci. Comput., 38 (2016), S508-S538. (PDF. Journal article link)
    • J. Shen, Y. Wang, and J. Xia, Fast structured direct spectral methods for differential equations with variable coefficients, I. The one-dimensional case, SIAM J. Sci. Comput., 38 (2016), pp. A28-A54. (PDF. Journal article link)
    • J. Vogel, J. Xia, S. Cauley, and V. Balakrishnan, Superfast divide-and-conquer method and perturbation analysis for structured eigenvalue solutions, SIAM J. Sci. Comput., 38 (2016), pp. A1358-A1382. (PDF. Journal article link)
    • A. Vogt, T. Reuschel, H.-D. Brüns, S. Le Borne, C. Schuster, On the Treatment of Arbitrary Boundary Conditions using a Fast Direct H-Matrix Solver in MoM, IEEE Transactions on Antennas & Propagation, Vol. 64 No. 08 (2016)
    • S. Wang. X. S. Li, F. H. Rouet, J. Xia, and M. V. de Hoop, A parallel geometric multifrontal solver using hierarchically semiseparable structure, ACM Trans. Math. Software, 42 (2016), Article 21. (PDF. Journal article link)
    • Y. Xi and J. Xia, On the stability of some hierarchical rank structured matrix algorithms, SIAM J. Matrix Anal. Appl., 37 (2016), pp. 1279-1303. (PDF. Journal article link)
  • 2015
    • Coulier, Pieter, Hadi Pouransari, and Eric Darve. The inverse fast multipole method: using a fast approximate direct solver as a preconditioner for dense linear systems. arXiv preprint arXiv:1508.01835 (2015).
    • R. Kriemann, S. Le Borne, H-FAINV: Hierarchically factored approximate inverse preconditioners, Comput. Vis. Sci. 17:135-150 (2015)
    • Pouransari, Hadi, Pieter Coulier, and Eric Darve. Fast hierarchical solvers for sparse matrices using low-rank approximation. arXiv preprint arXiv:1510.07363 (2015).
    • Wang, R., Li, Y., Mahoney, M. W., & Darve, E. (2015). Structured Block Basis Factorization for Scalable Kernel Matrix Evaluation. arXiv preprint arXiv:1505.00398.
    • Pouransari, Hadi, and Eric Darve. Optimizing the adaptive fast multipole method for fractal sets. SIAM Journal on Scientific Computing 37.2 (2015): A1040-A1066.
    • J. Xia, Z. Li, and X. Ye, Effective matrix-free preconditioning for the augmented immersed interface method, J. Comput. Phys., 303 (2015), pp. 295-312. (PDF. Journal article link)
    • J. Xia, Y. Xi, S. Cauley, and V. Balakrishnan, Fast sparse selected inversion, SIAM J. Matrix Anal. Appl., 36 (2015), pp. 1283-1314. (PDF. Journal article link)
  • 2014
    • Agullo, E., Bramas, B., Coulaud, O., Darve, E., Messner, M., & Takahashi, T. (2014). Task-based FMM for multicore architectures. SIAM Journal on Scientific Computing, 36(1), C66-C93.
    • Ambikasaran, Sivaram, and Eric Darve. The inverse fast multipole method. arXiv preprint arXiv:1407.1572 (2014).
    • Li, J. Y., Ambikasaran, S., Darve, E. F., & Kitanidis, P. K. (2014). A Kalman filter powered by H2-matrices for quasi-continuous data assimilation problems. Water Resources Research, 50(5), 3734-3749.
    • Y. Xi, J. Xia, S. Cauley, and V. Balakrishnan, Superfast and stable structured solvers for Toeplitz least squares via randomized sampling, SIAM J. Matrix Anal. Appl., 35 (2014), pp. 44-72. (PDF. Journal article link)
    • Y. Xi, J. Xia, and R. Chan, A fast randomized eigensolver with structured LDL factorization update, SIAM J. Matrix Anal. Appl., 35 (2014), pp. 974-996. (PDF. Journal article link)
  • 2013
    • Ambikasaran, Sivaram, and Eric Darve. An mathcal O (N log N) Fast Direct Solver for Partial Hierarchically Semi-Separable Matrices. Journal of Scientific Computing 57.3 (2013): 477-501.
    • Ambikasaran, S., Li, J. Y., Kitanidis, P. K., & Darve, E. (2013). Large-scale stochastic linear inversion using hierarchical matrices. Computational Geosciences, 17(6), 913-927.
    • Ambikasaran, S., Saibaba, A. K., Darve, E. F., & Kitanidis, P. K. (2013). Fast algorithms for Bayesian inversion. In Computational Challenges in the Geosciences (pp. 101-142). Springer New York.
    • Cecka, Cris, and Eric Darve. "Fourier-based fast multipole method for the Helmholtz equation." SIAM Journal on Scientific Computing 35.1 (2013): A79-A103.
    • J. Xia, Randomized sparse direct solvers, SIAM J. Matrix Anal. Appl., 34 (2013), pp. 197-227. (PDF. Journal article link)
    • J. Xia, Efficient structured multifrontal factorization for general large sparse matrices, SIAM J. Sci. Comput., 35 (2013), pp. A832-A860. (PDF. Journal article link)
  • 2012
    • S. Boerm, S. Le Borne, H-LU factorization in preconditioners for augmented Lagrangian and grad-div stabilized saddle point systems, International Journal for Numerical Methods in Fluids 68, 83-98 (2012), doi 10.1002/d.2495
    • S. Li, M. Gu, C. Wu, and J. Xia, New efficient and robust HSS Cholesky Factorization of SPD Matrices, SIAM J. Matrix Anal. Appl., 33 (2012), pp. 886-904. (PDF. Journal article link)
    • Messner, Matthias, Martin Schanz, and Eric Darve. Fast directional multilevel summation for oscillatory kernels based on Chebyshev interpolation. Journal of Computational Physics 231.4 (2012): 1175-1196.
    • Saibaba, A. K., Ambikasaran, S., Yue Li, J., Kitanidis, P. K., & Darve, E. F. (2012). Application of hierarchical matrices to linear inverse problems in geostatistics. Oil and Gas Science and Technology-Revue de l’IFP-Institut Francais du Petrole, 67(5), 857.
    • S. Wang, M. V. de Hoop, J. Xia, and X. S. Li, Massively parallel structured multifrontal solver for time-harmonic elastic waves in 3D anisotropic media, Geophys. J. Int., 191 (2012), pp. 346-366. (PDF. Journal article link)
    • S. Wang, J. Xia, M. V. de Hoop, and X. S. Li, Massively parallel structured direct solver for equations describing time-harmonic qP-polarized waves in TTI media, Geophys., 77 (2012), pp. T69-T82. (PDF. Journal article link)
    • J. Xia, On the complexity of some hierarchical structured matrix algorithms, SIAM J. Matrix Anal. Appl., 33 (2012), pp. 388-410.  (PDF. Journal article link)
    • J. Xia, Robust and efficient multifrontal solver for large discretized PDEs, High-Perform. Sci. Comput., M. W. Berry et al. (eds.), Springer (2012), pp. 199-217. (PDF. Journal article link)
    • J. Xia, A robust inner-outer HSS preconditioner, Numer. Linear Algebra Appl., 19 (2012), pp. 992-1016.  (PDF. Journal article link)
    • J. Xia, Y. Xi, and M. Gu, A superfast structured solver for Toeplitz linear systems via randomized sampling, SIAM J. Matrix Anal. Appl., 33 (2012), pp. 837-858. (PDF. Journal article link)
  • 2000 - 2011
    • S. Wang, M. V. de Hoop, and J. Xia, On 3D modeling of seismic wave propagation via a structured parallel multifrontal direct Helmholtz solver, Geophys. Prospect., 59 (2011), pp. 857-873.  (PDF. Journal article link)
    • J. Xia, S. Chandrasekaran, M. Gu, X. S. Li, Fast algorithms for hierarchically semiseparable matrices, Numer. Linear Algebra Appl., 17 (2010), pp. 953-976. (PDF. Journal article link)
    • Fong, William, and Eric Darve. The black-box fast multipole method. Journal of Computational Physics 228.23 (2009): 8712-8725.
    • L. Grasedyck, R. Kriemann, S. Le Borne, Domain Decomposition Based H-LU Preconditioning, Numerische Mathematik 112, 565-600 (2009), DOI 10.1007/s00211-009-0218-6
    • J. Xia, S. Chandrasekaran, M. Gu, X. S. Li, Superfast multifrontal method for large structured linear systems of equations, SIAM J. Matrix Anal. Appl., 31 (2009), pp. 1382-1411. (PDF. Journal article link)
    • S. Chandrasekaran, M. Gu, J. Xia, and J. Zhu, A fast QR algorithm for companion matrices, Oper. Theory Adv. Appl., Birkhauser Basel, 179 (2008), pp. 111-143. (PDF. Journal article link)
    • L. Grasedyck, R. Kriemann, S. Le Borne, Parallel blackbox H-LU preconditioning for elliptic boundary value problems, Comput. Vis. Sci. 11, 273-291 (2008)
    • S. Le Borne, Hierarchical matrix preconditioners for the Oseen equations, Comput. Vis. Sci. 11, 147-157 (2008)
    • S. Le Borne, S. Oliveira, F. Yang, H-matrix preconditioners for symmetric saddle point problems from meshfree discretizations, Numerical Linear Algebra with Applications 15, 911-924 (2008)
    • S. Chandrasekaran, M. Gu, X. Sun, J. Xia, and J. Zhu, A superfast algorithm for Toeplitz systems of linear equations, SIAM J. Matrix Anal. Appl., 29 (2007), pp. 1247-1266. (PDF. Journal article link)
    • S. Le Borne, S. Oliveira, Joint domain-decomposition H-LU preconditioners for saddle point problems, Electr. Trans. Num. Anal. 26, 285-298 (2007)
    • S. Chandrasekaran, M. Gu, and T. Pals, A fast ULV decomposition solver for hierarchically semiseparable representations, SIAM J. Matrix Anal. Appl., 28 (2006), pp. 603–622.
    • L. Grasedyck, S. Le Borne, H-matrix preconditioners in convection-dominated problems, SIAM J. Sci. Comp. 27, 1172 - 1183 (2006)
    • S. Le Borne, Multilevel hierarchical matrices, SIAM J. Mat. Anal. Appl. 28, 871 - 889 (2006)
    • W. Hackbusch, L. Grasedyck, S. Le Borne, Adaptive Geometrically Balanced Clustering of H-Matrices, Computing 73, 1-23 (2004)
    • S. Le Borne, H-matrices for convection-diffusion problems with constant convection, Computing 70, 261-274 (2003)
    • Darve, Eric. The fast multipole method I: error analysis and asymptotic complexity. SIAM Journal on Numerical Analysis 38.1 (2000): 98-128.
    • Darve, Eric. The fast multipole method: numerical implementation. Journal of Computational Physics 160.1 (2000): 195-240.