Michele Benzi's Selected Publications

Michele Benzi's Selected Publications

Note: If you would like to receive a copy of any of the papers not available online, please drop me a note.

RECENT PREPRINTS

  • M. Benzi, E. Haber and L. Taralli, A Preconditioning Technique for a Class of PDE-Constrained Optimization Problems, Math/CS Technical Report TR-2009-027, October 2009 (20 pages). Submitted.

  • Z.-Z. Bai, M. Benzi, and F. Chen, Modified HSS Iteration Methods for a Class of Complex Symmetric Linear Systems, Math/CS Technical Report TR-2009-021, July 2009. Revised October 2009 (18 pages). Submitted.

  • S. Hamilton, M. Benzi, and E. Haber, New Multigrid Smoothers for the Oseen Problem, Math/CS Technical Report TR-2009-001, January 2009. Revised November 2009 (18 pages). Submitted.

  • M. Benzi and X.-P. Guo, A Dimensional Split Preconditioner for Stokes and Linearized Navier-Stokes Equations, Math/CS Technical Report TR-2009-010, April 2009 (20 pages). Submitted. PLEASE NOTE: This manuscript corrects some mistakes in a previously posted one.

    ACCEPTED PAPERS (CURRENTLY IN PRESS)

  • M. Benzi, M. A. Olshanskii and Z. Wang, Modified Augmented Lagrangian Preconditioners for the Incompressible Navier-Stokes Equations, Math/CS Technical Report TR-2009-023. Revised November 2009 (26 pages). To appear in International J. of Numerical Methods in Fluids.

  • C. Zhang and M. Benzi, P-regular Splitting Iterative Methods for Non-Hermitian Positive Definite Linear Systems, Math/CS Technical Report TR-2009-014, May 2009. Revised August 2009 (15 pages). To appear in ETNA (Electronic Transactions on Numerical Analysis), Special Volume in honor of Richard Varga.

    SELECTED PUBLISHED PAPERS (REVERSE CHRONOLOGICAL ORDER BY YEAR)

    2009 (so far)

  • M. Benzi, L. Ferragut, M. Pennacchio and V. Simoncini, Solution of Linear Systems from an Optimal Control Problem Arising in Wind Simulation, Numerical Linear Algebra with Applications, November 2009 (published online).

  • M. Benzi, E. Haber, and L. Taralli, Multilevel Algorithms for Large-Scale Interior Point Methods, SIAM J. Scientific Computing, 31 (2009), pp. 4152-4175.

  • M. Benzi, A Generalization of the Hermitian and Skew-Hermitian Splitting Iteration, SIAM J. Matrix Analysis and Applications, 31 (2009), pp. 360-374.

  • S. Hamilton, M. Benzi, and J. Warsa, Negative-Flux Fixups in Discontinuous Finite Element S_N Transport, in Proceedings of the 2009 International Conference on Mathematics, Computational Methods & Reactor Physics (M&C 2009), Saratoga Springs, New York, 2009 [CD-ROM].

    2008

  • M. Benzi, Splittings of Symmetric Matrices and a Question of Ortega, Linear Algebra and its Applications, 429 (2008), pp. 2340-2343. Special Issue in Honor of Richard S. Varga (on the occasion of his 80th birthday).

  • M. Benzi and D. Bertaccini, Block Preconditioning of Real-Valued Iterative Algorithms for Complex Linear Systems, IMA Journal of Numerical Analysis, 28 (2008), pp. 598-618.

  • M. Benzi and A. J. Wathen, Some Preconditioning Techniques for Saddle Point Problems, in W. Schilders, H. A. van der Vorst and J. Rommes, eds., Model Order Reduction: Theory, Research Aspects and Applications, Springer-Verlag (Series: Mathematics in Industry), 2008, pp. 195-211.

  • M. A. Olshanskii and M. Benzi, An Augmented Lagrangian Approach to Linearized Problems in Hydrodynamic Stability, SIAM J. Scientific Computing, 30 (2008), pp. 1459-1473.

    2007

  • M. Benzi and J. Liu, An Efficient Solver for the Incompressible Navier-Stokes Equations in Rotation Form, SIAM J. Scientific Computing, 29 (2007), pp. 1959-1981.

  • M. Benzi and J. Liu, Block Preconditioning for Saddle Point Systems with Indefinite (1,1) Block, International Journal of Computer Mathematics, 84 (2007), pp. 1117-1129. Special issue on "Fast and Preconditioned Iterative Methods for Linear and Nonlinear Systems" (K. Chen, editor).

  • M. Benzi, M. Benzi and E. Seneta, Francesco Paolo Cantelli, International Statistical Review, 75(2), (2007), pp. 127-130.

  • M. Benzi and N. Razouk, Decay Bounds and O(N) Algorithms for Approximating Functions of Sparse Matrices, ETNA (Electronic Transactions on Numerical Analysis), 28 (2007), pp. 16-39. Special volume in honor of Gene Golub.

  • M. Benzi and B. Ucar, Block Triangular Preconditioners for M-matrices and Markov Chains, ETNA (Electronic Transactions on Numerical Analysis), 26 (2007), pp. 209-227.

  • M. Benzi and N. Razouk, On the Iwasawa Decomposition of a Symplectic Matrix, Applied Mathematics Letters, 20 (2007), pp. 260-265.

  • M. Noskov, M. Benzi, and M. D. Smooke. An Implicit Compact Scheme Solver for Two-Dimensional Multicomponent Flows, Computers & Fluids, 36 (2007), pp. 376-397.

    2006

  • M. Benzi and M. A. Olshanskii, An Augmented Lagrangian-Based Approach to the Oseen Problem, SIAM J. Scientific Computing, 28 (2006), pp. 2095-2113.

  • M. Benzi and B. Ucar, Product Preconditioning for Markov Chain Problems, in A. N. Langville and W. J. Stewart, eds., Proceedings of the 2006 Markov Anniversary Meeting (Charleston, SC, 12-14 June 2006), Boson Books, Raleigh, NC, 2006, pp. 239-256. This paper won the BEST PAPER AWARD.

  • M. Benzi and V. Simoncini, On the Eigenvalues of a Class of Saddle Point Matrices, Numerische Mathematik, 103 (2006), pp. 173-196.

  • M. Benzi and M. K. Ng. Preconditioned Iterative Methods for Weighted Toeplitz Least Squares Problems, SIAM J. Matrix Analysis and Applications, 27 (2006), pp. 1106-1124.

    2005

  • M. Benzi, Gianfranco Cimmino's Contributions to Numerical Mathematics, Atti del Seminario di Analisi Matematica, Dipartimento di Matematica dell'Universita` di Bologna. Volume Speciale: Ciclo di Conferenze in Memoria di Gianfranco Cimmino, Marzo-Aprile 2004, Tecnoprint, Bologna (2005), pp. 87-109.

  • M. Benzi, G. H. Golub, and J. Liesen. Numerical Solution of Saddle Point Problems, Acta Numerica, 14 (2005), pp. 1-137.

    2004

  • V. Simoncini and M. Benzi. Spectral Properties of the Hermitian and Skew-Hermitian Splitting Preconditioner for Saddle Point Problems, SIAM J. Matrix Analysis and Applications, 26 (2004), pp. 377-389.

  • J. Warsa, M. Benzi, T. Wareing and J. Morel. Preconditioning a Mixed Discontinuous Finite Element Method for Radiation Diffusion , Numerical Linear Algebra with Applications, 11 (2004), pp. 795-811.

  • M. Benzi and G. H. Golub. A Preconditioner for Generalized Saddle Point Problems, SIAM J. Matrix Analysis and Applications, 26 (2004), pp. 20-41.

  • M. Benzi. A Direct Projection Method for Markov Chains, Linear Algebra and its Applications, 386 (2004), pp. 27-49.

    2003

  • M. Benzi, M. J. Gander, and G. H. Golub. Optimization of the Hermitian and Skew-Hermitian Splitting Iteration for Saddle-Point Problems, BIT Numerical Mathematics 43 (2003), pp. 881-900.

  • M. Benzi and M. Tuma. A Robust Preconditioner with Low Memory Requirements for Large Sparse Least Squares Problems, SIAM J. Scientific Computing, 25 (2003), pp. 499-512.

  • M. Benzi and D. Bertaccini. Approximate Inverse Preconditioning for Shifted Linear Systems, BIT Numerical Mathematics, 43 (2003), pp. 231-244.

  • M. Benzi and M. Tuma. A Robust Incomplete Factorization Preconditioner for Positive Definite Matrices, Numerical Linear Algebra with Applications, 10 (2003), pp. 385-400.

    2002

  • M. Benzi. Preconditioning Techniques for Large Linear Systems: A Survey , Journal of Computational Physics, 182 (2002), pp. 418-477.

  • M. Benzi and M. Tuma. A Parallel Solver for Large-Scale Markov Chains , Applied Numerical Mathematics, 41 (2002), pp. 135-153.

    2001

  • M. Benzi, R. Kouhia and M. Tuma. Stabilized and Block Approximate Inverse Preconditioners for Problems in Solid and Structural Mechanics , Computer Methods in Applied Mechanics and Engineering, 190 (2001), pp. 6533-6554.

  • M. Benzi, A. Frommer, R. Nabben and D. B. Szyld. Algebraic Theory of Multiplicative Schwarz Methods , Numerische Mathematik, 89 (2001), pp. 605-639.

    2000

  • M. Benzi, J. C. Haws, and M. Tuma. Preconditioning Highly Indefinite and Nonsymmetric Matrices, SIAM J. Scientific Computing, 22 (2000), pp. 1333-1353.

  • M. Benzi, J. K. Cullum, and M. Tuma. Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method, SIAM J. Scientific Computing, 22 (2000), pp. 1318-1332.

  • M. Benzi and M. Tuma. Orderings for Factorized Sparse Approximate Inverse Preconditioners, SIAM J. Scientific Computing 21, 5 (2000), pp. 1851-1868.

    1999

  • M. Benzi and G. H. Golub. Bounds for the Entries of Matrix Functions with Applications to Preconditioning, BIT Numerical Mathematics 39, 3 (1999), pp. 417-438.

  • M. Benzi, W. D. Joubert, and G. Mateescu. Numerical Experiments with Parallel Orderings for ILU Preconditioners, ETNA (Electronic Transactions on Numerical Analysis), 8 (1999), pp. 88-114.

  • M. Benzi, J. Marin, and M. Tuma. A Two-Level Parallel Preconditioner Based on Sparse Approximate Inverses, in Iterative Methods in Scientific Computation IV, D. R. Kincaid and A. C. Elster, eds., IMACS Series in Computational and Applied Mathematics, Vol. 5, IMACS, New Brunswick, NJ (1999), pp. 167-178.

  • M. Benzi, D. B. Szyld, and A. van Duin. Orderings for Incomplete Factorization Preconditioning of Nonsymmetric Problems , SIAM J. Scientific Computing 20, 3 (1999), pp. 1652-1670.

  • M. Benzi and M. Tuma. A Comparative Study of Sparse Approximate Inverse Preconditioners , Applied Numerical Mathematics 30, 2-3 (1999), pp. 305-340.

    1998

  • M. Benzi, R. Kouhia, and M. Tuma. An Assessment of Some Preconditioning Techniques in Shell Problems , Communications in Numerical Methods in Engineering 14 (1998), pp. 897-906.

  • M. Benzi and M. Tuma. Numerical Experiments with Two Approximate Inverse Preconditioners , BIT Numerical Mathematics 38, 2 (1998), pp. 234-241.

  • M. Benzi and M. Tuma. A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems , SIAM J. Scientific Computing 19, 3 (1998), pp. 968-994. This paper won the SIAM OUTSTANDING PAPER PRIZE in 2001.

    1997

  • G. Alleon, M. Benzi and L. Giraud. Sparse Approximate Inverse Preconditioning for Dense Linear Systems Arising in Computational Electromagnetics , Numerical Algorithms 16, 1 (1997), pp. 1-15.

  • M. Benzi, H. Choi, and D. B. Szyld. Threshold Orderings for Preconditioning Nonsymmetric Problems , in G. H. Golub, S. H. Lui, F. T. Luk and R. J. Plemmons, editors, Proceedings of the Workshop on Scientific Computing, Hong Kong, 10-12 March 1997, pp. 159-165, Springer Verlag (1997).

  • M. Benzi. Remarks on the Numerical Solution of Certain Linear Complementarity Problems , J. Computational and Applied Mathematics 83 (1997), pp. 137-143.

  • M. Benzi and D. B. Szyld. Existence and Uniqueness of Splittings for Stationary Iterative Methods with Applications to Alternating Methods , Numerische Mathematik 76, 3 (1997), pp. 309-321.

    1996

  • M. Benzi, C. D. Meyer, and M. Tuma. A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method , SIAM J. Scientific Computing 17, 5 (1996), pp. 1135-1149.

  • M. Benzi and M. Tuma. A Comparison of Some Preconditioning Techniques for General Sparse Matrices , in S. Margenov and P. Vassilevski, editors, Iterative Methods in Linear Algebra, II, IMACS Series in Computational and Applied Mathematics, Vol. 3, pp. 191-203, IMACS, New Brunswick, NJ, 1996.

    1995

  • M. Benzi and C. D. Meyer. A Direct Projection Method for Sparse Linear Systems , SIAM J. Scientific Computing 16, 5 (1995), pp. 1159-1176.

  • M. Benzi and T. Dayar. The Arithmetic Mean Method for Finding the Stationary Vector of Markov Chains , Parallel Algorithms and Applications 6 (1995), pp. 25-37.

  • M. Benzi, F. Sgallari, and G. Spaletta. A Parallel Block Projection Method of the Cimmino Type for Finite Markov Chains , in W. J. Stewart, editor, Computations with Markov Chains: Proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, Kluwer Academic Publishers, pp. 65-80, Boston, MA, 1995.

    1994

  • M. Benzi and C. D. Meyer. An Explicit Preconditioner for the Conjugate Gradient Method, in J. D. Brown, M. T. Chu, D. C .Ellison and R. J. Plemmons, editors, Proceedings of the Cornelius Lanczos International Centenary Conference, SIAM, pp. 294-296, Philadelphia, PA, 1994.

    1993

  • M. Benzi. Solution of Equality-Constrained Quadratic Programming Problems by a Projection Iterative Method , Rendiconti di Matematica e delle sue Applicazioni, VII, 13 (1993), pp. 275-296.

    Return to Michele's homepage

    Last updated November 22, 2009.