Michele Benzi's Selected Publications

Michele Benzi's Publications


Note: This page contains most of my research publications. If you would like to receive a copy of any of the papers not available online, please drop me a note.


RECENT PREPRINTS

  • F. P. A. Beik and M. Benzi, Iterative Methods for Double Saddle Point Systems, Math/CS Technical Report, March 2017 (29 pages). Submitted.


    PUBLISHED/ACCEPTED PAPERS (REVERSE CHRONOLOGICAL ORDER BY YEAR)

    2017 (so far)

  • E. Estrada and M. Benzi, What is the Meaning of the Graph Energy After All?, arXiv:1704.00779v1 [math.CO], 3 April 2017. Revised, June 2017 (10 pages). To appear in Discrete Applied Mathematics.

  • M. Arioli and M. Benzi, A Finite Element Method for Quantum Graphs, Math/CS Technical Report TR-2015-009, October 2015. Revised, October 2016, January and March 2017 (45 pages). To appear in IMA Journal of Numerical Analysis.

  • F. P. A. Beik, M. Benzi, and S.-H. A. Chaparpordi, On Block Diagonal and Block Triangular Iterative Schemes and Preconditioners for Stabilized Saddle Point Problems, Journal of Computational and Applied Mathematics, 326 (2017), pp. 15-30.

  • M. Benzi, Book Review: Andre'-Louis Cholesky: Mathematician, Topographer and Army Officer, by Claude Brezinski and Dominique Tournes, The Mathematical Intelligencer, 39 (2017), pp. 99-101.

  • Z.-Z. Bai and M. Benzi, Regularized HSS Iteration Methods for Saddle-Point Linear Systems, BIT Numerical Mathematics, 57 (2017), pp. 287-311.

  • I. Chen, M. Benzi, H. H. Chang, and V. S. Hertzberg, Dynamic Communicability and Epidemic Spread: A Case Study on an Empirical Dynamic Contact Network, Journal of Complex Networks, 5 (2017), pp. 274-302.

  • M. Benzi, T. Evans, S. Hamilton, M. Lupo Pasini, and S. Slattery, Analysis of Monte Carlo Accelerated Iterative Methods for Sparse Linear Systems, Numerical Linear Algebra with Applications, 24 (2017), DOI:10.1002/nla.2088 (18 pages).

  • E. Estrada and M. Benzi, Core-satellite Graphs: Clustering, Assortativity and Spectral Properties, Linear Algebra and its Applications, 517 (2017), pp. 30-52.

  • M. Benzi and V. Simoncini, Approximation of Functions of Large Matrices with Kronecker Structure, Numerische Mathematik, 135 (2017), pp. 1-26.

    2016

  • M. Benzi and B. Ucar, Preconditioning Techniques Based on the Birkhoff-von Neumann Decomposition, Computational Methods in Applied Mathematics, 17 (2016), pp. 201-215.

  • M. Benzi, Localization in Matrix Computations: Theory and Applications, in M. Benzi and V. Simoncini (Eds.), ``Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications (Cetraro, Italy 2015)", Lecture Notes in Mathematics, Volume 2173, Springer, New York, 2016, pp. 211-317.

  • F. Arrigo, M. Benzi, and C. Fenu, Computation of Generalized Matrix Functions, SIAM Journal on Matrix Analysis and Applications, 37 (2016), pp. 836-860.

  • F. Arrigo and M. Benzi, Edge Modification Criteria for Enhancing the Communicability of Digraphs, SIAM Journal on Matrix Analysis and Applications, 37 (2016), pp. 443-468.

  • M. Benzi, S. Deparis, G. Grandperrin and A. Quarteroni, Parameter Estimates for the Relaxed Dimensional Factorization Preconditioner and Application to Hemodynamics, Computer Methods in Applied Mechanics and Engineering, 300 (2016), pp. 129-145.

  • F. Arrigo and M. Benzi, Updating and Downdating Techniques for Optimizing Network Communicability, SIAM Journal on Scientific Computing, 38 (2016), pp. B25-B49.

    2015

  • M. Benzi and V. Simoncini, Decay Bounds for Functions of Hermitian Matrices with Banded or Kronecker Structure, SIAM Journal on Matrix Analysis and Applications, 36 (2015), pp. 1263-1282.

  • M. Benzi and C. Klymko, On the Limiting Behavior of Parameter-Dependent Network Centrality Measures, SIAM Journal on Matrix Analysis and Applications, 36 (2015), pp. 686-706.

    2014

  • E. Estrada and M. Benzi, A Walk-Based Measure of Balance in Signed Networks: Detecting Lack of Balance in Social Networks, Physical Review E, 90 (2014), 042802 [10 pages].

  • M. Benzi and P. Boito, Decay Properties for Functions of Matrices over C*-Algebras, Linear Algebra and its Applications (Special Issue on Matrix Functions), 456 (2014), pp. 174-198.

  • M. Benzi and E. Toscano, Mauro Picone, Sandro Faedo, and the Numerical Solution of Partial Differential Equations in Italy (1928-1953), Numerical Algorithms, 66(1) (2014), pp. 105-145.

  • M. Benzi, A Note on Walk Entropies in Graphs, Linear Algebra and its Applications, 445 (2014), pp. 395-399.

    2013

  • M. Benzi and C. Klymko, Total Communicability as a Centrality Measure, Journal of Complex Networks, 1(2) (2013), pp. 124-149.

  • M. Benzi and V. Kuhlemann, Chebyshev Acceleration of the GeneRank Algorithm, ETNA (Electronic Transactions on Numerical Analysis), 40 (2013), pp. 311-320.

  • M. Benzi and Z. Wang, A Parallel Implementation of the Modified Augmented Lagrangian Preconditioner for the Incompressible Navier-Stokes Equations, Numerical Algorithms, 64 (2013), pp. 73-84.

  • E. Estrada and M. Benzi, Atomic Displacements Due to Spin-Spin Repulsion in Conjugated Alternant Hydrocarbons, Chemical Physics Letters, 568-569 (2013), pp. 184-189.

  • M. Benzi, P. Boito and N. Razouk, Decay Properties of Spectral Projectors with Applications to Electronic Structure, SIAM Review, 55 (2013), pp. 3-64.

  • Z.-Z. Bai, M. Benzi, F. Chen, and Z.-Q. Wang, Preconditioned MHSS Iteration Methods for a Class of Block Two-by-Two Linear Systems with Applications to Distributed Control Problems, IMA Journal of Numerical Analysis, 33 (2013), pp. 343-369.

  • M. Benzi, E. Estrada and C. Klymko, Ranking Hubs and Authorities Using Matrix Functions, Linear Algebra and its Applications, 438 (2013), pp. 2447-2474.

    2012

  • M. Benzi, M. A. Olshanskii, L. G. Rebholz and Z. Wang, Assessment of a Vorticity Based Solver for the Navier-Stokes Equations, Computer Methods in Applied Mechanics and Engineering, 247-248 (2012), pp. 216-225.

  • Y. Wang, E. Agichtein and M. Benzi, TM-LDA: Efficient Online Modeling of the Latent Topic Transitions in Social Media, Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD'12), Association for Computing Machinery, New York, NY (2012), pp. 123-131.

  • E. Estrada, N. Hatano, and M. Benzi, The Physics of Communicability in Complex Networks, Physics Reports, 514 (2012), pp. 89-119.

    2011

  • M. Benzi and V. Kuhlemann, Restricted Additive Schwarz Methods for Markov Chains, Numerical Linear Algebra with Applications, 18 (2011), pp. 1011-1029.

  • M. Benzi and Z. Wang, Analysis of Augmented Lagrangian-Based Preconditioners for the Steady Incompressible Navier-Stokes Equations, SIAM J. Scientific Computing, 33 (2011), pp. 2761-2784.

  • M. Benzi, E. Haber and L. Taralli, A Preconditioning Technique for a Class of PDE-Constrained Optimization Problems, Advances in Computational Mathematics, 35 (2011), pp. 149-173.

  • M. Benzi, M. K. Ng, Q. Niu and Z. Wang, A Relaxed Dimensional Factorization Preconditioner for the Incompressible Navier-Stokes Equations, Journal of Computational Physics, 230 (2011), pp. 6185-6202.

  • M. Benzi, M. A. Olshanskii and Z. Wang, Modified Augmented Lagrangian Preconditioners for the Incompressible Navier-Stokes Equations, International Journal for Numerical Methods in Fluids, 66 (2011), pp. 486-508.

  • M. Benzi and M. A. Olshanskii, Field-of-Values Convergence Analysis of Augmented Lagrangian Preconditioners for the Linearized Navier-Stokes Problem, SIAM J. Numerical Analysis, 49 (2011), pp. 770-788.

  • Z.-Z. Bai, M. Benzi and F. Chen, On Preconditioned MHSS Iteration Methods for Complex Symmetric Linear Systems, Numerical Algorithms, 56 (2011), pp. 297-317.

  • M. Benzi and X.-P. Guo, A Dimensional Split Preconditioner for Stokes and Linearized Navier-Stokes Equations, Applied Numerical Mathematics, 61 (2011), pp. 66-76.

    2010

  • 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, 17 (2010), pp. 895-915.

  • M. Benzi and P. Boito, Quadrature Rule-Based Bounds for Functions of Adjacency Matrices, Linear Algebra and its Applications, 433 (2010), pp. 637-652.

  • Z.-Z. Bai, M. Benzi, and F. Chen, Modified HSS Iteration Methods for a Class of Complex Symmetric Linear Systems, Computing, 87 (2010), pp. 93-111.

  • S. Hamilton, M. Benzi and E. Haber, New Multigrid Smoothers for the Oseen Problem, Numerical Linear Algebra with Applications, 17 (2010), pp. 557-576.

  • C. Zhang and M. Benzi, P-regular Splitting Iterative Methods for Non-Hermitian Positive Definite Linear Systems, ETNA (Electronic Transactions on Numerical Analysis), 36 (2009-2010), pp. 39-53. Special Volume in honor of Richard Varga.

    2009

  • 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, Proceedings of the International Conference on Mathematics, Computational Methods & Reactor Physics 2009 (M&C 2009), American Nuclear Society, Vol. 4 (2009), pp. 2529-2538, Saratoga Springs, NY, 2009.

    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.


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    Last updated June 17, 2017.