Contents


Krylov subspace iterative system solvers
Preconditioning and structured matrices
Eigenvalue/Singular value problems
Functions of Matrices and Matrix Equations
Data Science
Applications
Miscellaneous




Krylov subspace iterative system solvers (reverse chronological order)

  1. Nick Gould and V. Simoncini,
    Error estimates for iterative algorithms for minimizing regularized quadratic subproblems
    Optimization Methods and Software. v.35 (2), 2020, pp.304-328. DOI:10.1080/10556788.2019.1670177

  2. Giulia Sacchi and V. Simoncini
    A new GMRES convergence analysis for localized invariant subspace ill-conditioning.
    SIAM J. Matrix Anal. Appl., 40(2), 542-563 (2019). DOI: https://doi.org/10.1137/17M1141291

  3. V. Simoncini and Daniel B. Szyld ,
    On the Superlinear Convergence of MINRES
    Proceedings ENUMATH 2011, Numerical Mathematics and Advanced Applications 2011, pp. 733-740, Springer (2013).

  4. Lars Eldén V. Simoncini
    Solving ill-posed Linear Systems with GMRES and a singular Preconditioner
    SIAM J. Matrix Anal. Appl., v.33 (4), (2012), pp.1369--1394.

  5. Gianluca Barbella, Federico Perotti and V. Simoncini
    Block Krylov subspace methods for the computation of structural response to turbulent wind
    Comput. Meth. Applied Mech. Eng. (CMAME), (2011), v. 200(23-24), pp. 2067-2082.

  6. V. Simoncini and Daniel B. Szyld ,
    Interpreting IDR as a Petrov-Galerkin method
    SIAM J. Scientific Computing. v.32, n.4, pp.1898-1912 (2010).

  7. V. Simoncini,
    On a non-stagnation condition for GMRES and application to saddle point matrices
    ETNA Electr. J. Numerical Analysis, v.37, pp. 202-213 (2010)

  8. V. Simoncini,
    The Extended Krylov subspace for parameter dependent systems
    Applied Num. Math. v.60 n.5 (2010) 550-560.

  9. V. Simoncini and Daniel B. Szyld ,
    New conditions for non-stagnation of minimal residual methods
    Numerische Mathematik, v. 109, n.3 (2008), pp. 477-487.

  10. V. Simoncini and Daniel B. Szyld ,
    Recent computational developments in Krylov Subspace Methods for linear systems
    Numerical Linear Algebra w/Appl., v. 14, n.1 (2007), pp.1-59.

  11. V. Simoncini and Daniel B. Szyld ,
    Relaxed Krylov subspace approximation
    PAMM v. 5, n.1 (Dec. 2005), pp.797-800.

  12. Guiding Gu and V. Simoncini,
    Numerical solution of parameter-dependent linear systems
    J. Numer. Linear Algebra w/Appl. v. 12, n. 9 (2005), pp. 923-940.

  13. V. Simoncini and Daniel B. Szyld ,
    The effect of non-optimal bases on the convergence of Krylov Subspace Methods
    Numer. Math. v. 100, n.4 (2005), pp. 711-733.

  14. V. Simoncini and D. Szyld,
    On the occurrence of Superlinear Convergence of Exact and Inexact Krylov Subspace Methods
    SIAM Review v. 47, n.2 (2005), pp. 247-272.

  15. V. Simoncini and M. Pennacchio,
    The behavior of symmetric Krylov subspace methods for solving M x= (M - γ I)v.
    Linear Algebra and Appl., v.380 (2004), pp.53-71.

  16. V. Simoncini and D. B. Szyld,
    Theory of Inexact Krylov Subspace Methods and Applications to Scientific Computing
    SIAM J. Scient. Computing, v.25, n.2 (2003), pp. 454-477.

  17. V. Simoncini,
    Restarted Full Orthogonalization Method for shifted linear systems,
    BIT Numerical Mathematics, v.43, n.2 (2003) pp. 459-466.

  18. V. Simoncini and D. B. Szyld,
    Flexible Inner-Outer Krylov Subspace Methods
    SIAM J. Numer. Analysis, v.40 (6) 2003, pp. 2219-2239.

  19. V. Simoncini and F. Perotti,
    On the numerical solution of (λ² A + λ B + C) x = b and application to structural dynamics
    SIAM J. Sci. Comput. v. 23 n.6 (2002) pp. 1876-1898.

  20. V. Simoncini,
    On the convergence of restarted Krylov subspace methods
    SIAM J. Matrix Analysis and Appl., v.22, n.2, (2000), pp. 430--452.

  21. V. Simoncini,
    A new variant of restarted GMRES
    Numerical Linear Algebra with Appl., v. 6 (1999), pp. 61-77.

  22. V. Simoncini,
    Linear systems with a quadratic parameter and application to structural dynamics
    in Iterative Methods in Scientific Computation II,
    IMACS Series in Computational and Applied Mathematics, D. Kincaid and A. Elster, eds.,
    vol. 5, 1999, pp. 451-461.


  23. V. Simoncini,
    A stabilized QMR version of block BiCG
    SIAM J. Matrix Analysis and Appl., v. 18-2 (1997)

  24. E. Kasenally and V. Simoncini,
    Analysis of a minimum perturbation algorithm for nonsymmetric linear systems
    SIAM J. Numerical Analysis, v. 34 (1) (1997)

  25. V. Simoncini and E. Gallopoulos,
    A hybrid block GMRES method for nonsymmetric systems with multiple right-hand sides
    J. Comput. Applied Math. (1996) pp. 457-469.

  26. V. Simoncini and E. Gallopoulos,
    Convergence Properties of Block GMRES and Matrix Polynomials
    Linear Algebra and Appl., v. 247 (1996), pp. 97-119.

  27. V. Simoncini and E. Gallopoulos,
    An Iterative Method for Nonsymmetric Systems with Multiple Right-hand Side
    SIAM J. Scient. Computing, v. 15 (1995) pp.917-933.

  28. E. Gallopoulos and V. Simoncini,
    Iterative solution of multiple linear systems: Theory, practice, parallelism and applications
    Advances in Parallel and Vector Processing for Structural Mechanics:
    Proc. Second Int'l. Conf. on Computational Structures Technology, eds. B.H.V. Topping and M. Papadrakakis
    (1994), pp. 47--51.

  29. T. F. Chan, E. Gallopoulos, V. Simoncini, T. Szeto and C. H. Tong
    A Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems
    SIAM J. Scient. Computing, v. 15 (1994) pp. 338-347.




    Preconditioning and structured matrices (reverse chronological order)

  30. Margherita Porcelli , V. Simoncini and Martin Stoll
    Preconditioning PDE-constrained optimization with L^1-sparsity and control constraints
    pp. 1-22, Dipartimento di Matematica, Universita' di Bologna, Nov 2016. (Opt Online n.5734) To appear in Computers & Mathematics w/Appl. DOI 10.1016/j.camwa.2017.04.033

  31. Davide Palitta and V. Simoncini
    matrix-equation-based strategies for convection-diffusion equations
    BIT Numerical Mathematics, 56(2), (2016), 751-776. DOI: 10.1007/s10543-015-0575-8

  32. Margherita Porcelli , V. Simoncini and Mattia Tani
    Preconditioning of active-set Newton methods for PDE-Constrained optimal control problems
    SIAM J. Sci. Comput. 37-5 (2015), pp. S472-S502

  33. Benedetta Morini , V. Simoncini and Mattia Tani
    A comparison of reduced and unreduced symmetric KKT systems arising from Interior Point methods
    Computational Optimization and Applications, v.68(1), 2017, pp.1-27. DOI: 10.1007/s10589-017-9907-8

  34. Benedetta Morini , V. Simoncini and Mattia Tani
    Spectral estimates for unreduced symmetric KKT systems arising from Interior Point methods
    Numerical Linear Algebra w/Appl. Volume 23, Issue 5 (2016), pp. 776–800. DOI: 10.1002/nla.2054

  35. Wolfgang Krendl, V. Simoncini and Walter Zulehner,
    Efficient preconditioning for an optimal control problem with the time-periodic Stokes equations
    Proceedings ENUMATH 2013, Numerical Mathematics and Advanced Applications, Springer 2015, pp.479-488.

  36. M. Tani and V. Simoncini,
    Refined spectral estimates for preconditioned saddle point linear systems in a non-standard inner product
    ANZIAM J., v.54, pp.C291--C308 (2013), Proceedings of the 16th Biennial Computational Techniques and Applications Conference, CTAC-2012.

  37. Wolfgang Krendl, V. Simoncini and Walter Zulehner,
    Stability Estimates and Structural Spectral Properties of Saddle Point Problems
    Numerische Mathematik: Volume 124, Issue 1 (2013), Page 183-213.

  38. V. Simoncini
    Reduced order solution of structured linear systems arising in certain PDE-constrained optimization problems
    Computational Optimization and Applications, 53 (2), (2012), pp. 591-617.

  39. D. Sesana and V. Simoncini
    Spectral analysis of inexact constraint preconditioning for symmetric saddle point matrices
    Linear Algebra and Appl., v.438 (2013), pp.2683-2700.

  40. Micol Pennacchio and V. Simoncini
    Fast structured AMG Preconditioning for the bidomain model in electrocardiology
    SIAM J. Scient. Computing., v. 33, n.2, pp. 721-745 (2011).

  41. David J. Silvester , and V. Simoncini
    EST_MINRES: An Optimal Iterative Solver for Symmetric Indefinite Systems stemming from Mixed Approximation
    ACM Transactions on Mathematical Software. v.37, n.4, pp.42:1--42:22, (2011).

  42. Maxim A. Olshanskii, and V. Simoncini
    Acquired clustering properties and solution of certain saddle point systems
    SIAM. J. Matrix Anal. and Appl. Volume 31, Issue 5, pp. 2754-2768 (2010).

  43. Micol Pennacchio and V. Simoncini,
    Non-symmetric Algebraic Multigrid Preconditioners for the Bidomain Reaction--Diffusion system
    Proceedings ENUMATH 2009, Numerical Mathematics and Advanced Applications 2009, 729-736, Springer (2010).

  44. Micol Pennacchio and V. Simoncini,
    Algebraic Multigrid Preconditioners for the Bidomain Reaction--Diffusion system
    Applied Numerical Mathematics. Volume 59, Issue 12, Dec. 2009, pp. 3033-3050.

  45. Nick Gould and V. Simoncini,
    Spectral Analysis of saddle point matrices with indefinite leading blocks
    SIAM J. Matrix Analysis Appl., Volume 31, Issue 3, pp. 1152-1171 (2009).

  46. Micol Pennacchio and V. Simoncini,
    Substructuring Preconditioners for Mortar Discretization of a Degenerate Evolution Problem
    Journal of Scientific Computing, v. 36, n. 3, September 2008, pp.391-419.

  47. Michele Benzi and V. Simoncini
    On the Eigenvalues of a Class of Saddle Point Matrices
    Numerische Mathematik, v. 103, n.2 (2006), pp. 173-196.

  48. V. Simoncini and M. Benzi,
    Spectral Properties of the Hermitian and Skew-Hermitian Splitting Preconditioner for Saddle Point Problems
    SIAM J. Matrix Analysis and Appl., v.26, n.2 (2004), pp. 377-389.

  49. V. Simoncini,
    Block triangular preconditioners for Symmetric Saddle-Point problems
    Applied Num. Math. v.49, n.1 (2004), pp. 63-80.

  50. M. Pennacchio and V. Simoncini,
    Efficient algebraic solution of reaction--diffusion systems for the cardiac excitation process
    J. Comput. Applied Math., v.145 (1) (2002), pp.49-70.


  51. M. Rozlozník and V. Simoncini,
    Krylov Subspace Methods for Saddle Point Problems with Indefinite Preconditioning
    SIAM J. Matrix Analysis and Appl., v.24 n.2 (2002) pp. 368-391.

  52. I. Perugia and V. Simoncini,
    Block-diagonal and indefinite symmetric preconditioners for mixed finite element formulations
    Numerical Linear Algebra with Appl. v. 7, n.7--8 (2000), pp. 585--616.

  53. I. Perugia, V. Simoncini and M. Arioli,
    Linear Algebra methods in a mixed approximation of magnetostatic problems
    SIAM J. Sci. Comput., v.21, n.3, (1999) pp.1085--1101.



    Eigenvalue/Singular value problems (reverse chronological order)

  54. Sarah W. Gaaf and V. Simoncini
    Approximating the leading singular triplets of a large matrix function
    Applied Numerical Mathematics 113C (2017) pp. 26-43 DOI: 10.1016/j.apnum.2016.10.015

  55. V. Simoncini and Daniel B. Szyld ,
    On the field of values of oblique projections
    Linear Algebra and its Applications. v.433 n.4, pp. 810-818 (2010).

  56. Volker Mehrmann , Christian Schröder and V. Simoncini
    An Implicitly-restarted Krylov Method for Real Symmetric/Skew-Symmetric Eigenproblems
    Linear Algebra and Appl., 436 (10), (2012), pp. 4070-4087.
    The software associated with this paper is available here

  57. V. Simoncini,
    Variable Accuracy of Matrix-Vector Products in Projection Methods for Eigencomputation SIAM J. Numerical Analysis v. 43, n.3 (2005), pp. 1155-1174.

  58. Constantine N. Bekas , Stratis Gallopoulos and V. Simoncini,
    Pseudospectra Computation of Large Matrices
    January 2004, p.1-26.
  59. V. Simoncini,
    Algebraic formulations for the solution of the nullspace-free eigenvalue problem using the inexact Shift-and-Invert Lanczos method
    Numer. Linear Algebra w/Appl. v. 10, n.4 (2003), pp. 357-375.
  60. C. Bekas, E. Kokiopoulou, E. Gallopoulos and V. Simoncini,
    Parallel Computation of Pseudospectra using Transfer Functions on a {\tt MATLAB-MPI} Cluster Platform}
    D. Kranzlmueller, P. Kacsuk, J. Dongarra, J. Volkert (Eds.):
    "Recent Advances in Parallel Virtual Machine and Message Passing Interface" Proc. 9th European PVM/MPI Users' Group Meeting, Springer-Verlag, Lecture Notes in Computer Science,
    Vol. 2474, pp.199-207, Linz, Austria, September 29-October 2, 2002.
  61. V. Simoncini and L. Eldén,
    Inexact Rayleigh quotient-type methods for eigenvalue computations
    BIT Numerical Mathematics, v. 42, n.1 (2002), pp. 159-182.
  62. V. Simoncini,
    Remarks on non-linear spectral perturbation
    BIT Numerical Mathematics, v. 39, n.2 (1999), pp.350-365.
  63. V. Simoncini and E. Gallopoulos,
    Transfer functions and Resolvent norm approximation of large matrices
    ETNA, v. 7 (1998), pp. 190--201.
  64. V. Simoncini,
    A matrix analysis of Arnoldi and Lanczos methods
    Numer. Math. v. 81 n. 1 (1998), pp.125-141.
  65. V. Simoncini and E. Sjostrom,
    An algorithm for approximating the singular triplets of complex symmetric matrices
    Num. Linear Algebra with Appl., v. 4 (6) (1997) pp.469-489.
  66. V. Simoncini,
    An Iterative Procedure for Computing the Null Basis
    in Iterative Methods in Linear Algebra, II,
    IMACS Series in Computational and Applied Mathematics, S.~Margenov and P.~Vassilevski,
    eds., vol.~3, 1996, pp. 413-423.

  67. V. Simoncini and M. Sadkane,
    Arnoldi-Riccati method for large eigenvalue problems
    BIT Numerical Mathematics, v. 36 (3) (1996) pp. 579-594.

  68. V. Simoncini,
    Ritz and Pseudo-Ritz Values Using Matrix Polynomials
    Linear Algebra and Appl., v. 241-3, pp. 787-802 (1996).




    Functions of Matrices and Matrix Equations (reverse chronological order)

  69. Lorenzo Piccinini , and V. Simoncini
    Truncated LSQR for matrix least squares problems and application to Dictionary Learning
    pp. 1-22, Dipartimento di Matematica, Universita' di Bologna, February 2024.

  70. Daniele Toni , and V. Simoncini
    On some structural properties of generalized Lyapunov eigenproblems and application to operator preconditioning
    pp. 1-20, Dipartimento di Matematica, Universita' di Bologna, January 2023.

  71. Margherita Porcelli, and V. Simoncini
    Numerical solution of a class of quasi-linear matrix equations
    Linear Algebra and Its Applications 664C (2023) pp. 349-368. https://doi.org/10.1016/j.laa.2023.01.024

  72. V. Simoncini and Yue Hao
    Analysis of the truncated conjugate gradient method for linear matrix equations
    pp. 1-24, Dipartimento di Matematica, Universita' di Bologna, February 2022. HAL archive hal-03579267. To appear in SIAM J. Matrix Analysis and Appl.

  73. Julian Henning, Davide Palitta , V. Simoncini and Karsten Urban
    A Very Weak Space-Time Variational Formulation for the Wave Equation: Analysis and Efficient Numerical Solution
    ESAIM: M2AN, 56(4) July-August 2022, pp. 1173 - 1198.

  74. Davide Palitta , Stefano Pozza and V. Simoncini
    The short-term rational Lanczos method and applications
    SIAM J. Sci. Comput., 44 (4), A2843-A2870, 2022. https://doi.org/10.1137/21M1403254.

  75. Stefano Pozza and V. Simoncini
    Functions of Rational Krylov Space matrices and their decay properties
    Numerische Mathematik, 148 (1), 2021, pp. 99-126. DOI: 10.1007/s00211-021-01198-4



  76. Yue Hao and V. Simoncini
    The Sherman-Morrison-Woodbury formula for generalized linear matrix equations and applications
    pp. 1-20, Dipartimento di Matematica, Universita' di Bologna, July 2020. HAL archive hal-02902455.
    To appear in Numer. Linear Algebra w/Appl. DOI: 10.1002/nla.2384

  77. V. Simoncini
    Numerical solution of a class of third order tensor linear equations
    Bollettino UMI, 13 (3), 2020, pp.429-439. DOI: 10.1007/s40574-020-00247-4

  78. Gerhard Kirsten and V. Simoncini
    Order reduction methods for solving large-scale differential matrix Riccati equations
    SIAM J. Scient. Computing, v. 42 (4), 2020, pages A2182-A2205. DOI: 10.1137/19M1264217

  79. Julian Henning Davide Palitta, V. Simoncini and Karsten Urban
    Matrix oriented reduction of space-time Petrov-Galerkin variational problems.
    , In ``Numerical Mathematics and Advanced Applications, ENUMATH 2019'' Proceedings, Springer (2021), pp. 1049-1058.

  80. Davide Palitta and V. Simoncini
    Optimality properties of Galerkin and Petrov-Galerkin methods for linear matrix equations
    pp.1-15, Dipartimento di Matematica, Universita' di Bologna, August 2019. arXiv:1908.06016 [math.NA] . To appear in Vietnam Journal of Mathematics.

  81. V. Simoncini
    On the numerical solution of a class of systems of linear matrix equations
    IMA J. Numerical Analysis, v. 44 (1), 2020, 207-225. DOI: 10.1093/imanum/dry083

  82. Davide Palitta and V. Simoncini
    Numerical methods for large-scale Lyapunov equations with symmetric banded data arXiv: 1711.04187 [math.NA] .
    SIAM J. Scientific Computing, v.40 (5), pp.A3581--A3608 (2018). https://doi.org/10.1137/17M1156575

  83. Stefano Pozza and V. Simoncini
    Decay bounds for functions of banded non-Hermitian matrices
    BIT Numerical Analysis, 59(4), pp. 969-986 (2019). DOI: https://doi.org/10.1007/s10543-019-00763-6

  84. Davide Palitta and V. Simoncini
    Computationally enhanced projection methods for symmetric Sylvester and Lyapunov matrix equations
    J. Computational and Applied Mathematics, 330 (2018) 648-659.

  85. V. Simoncini
    Analysis of the rational Krylov subspace projection method for large-scale algebraic Riccati equations
    SIAM J. Matrix Analysis and Appl. 37-4 (2016), pp. 1655-1674. http://dx.doi.org/10.1137/16M1059382

  86. Catherine E. Powell , David Silvester , and V. Simoncini
    An efficient reduced basis solver for stochastic Galerkin matrix equations
    SIAM J. Scientific Computing, 39 (1), (2017), pp.A141-A163. DOI:10.1137/15M1032399

  87. Michele Benzi and V. Simoncini
    Approximation of functions of large matrices with Kronecker structure
    Numerische Mathematik 135(1) (2017) pp.1-26. DOI: 10.1007/s00211-016-0799-9

  88. Michele Benzi and V. Simoncini
    Decay bounds for functions of Hermitian matrices with banded or Kronecker structure
    SIAM. J. Matrix Anal. Appl. 36-3 (2015), pp. 1263-1282 http://dx.doi.org/10.1137/151006159

  89. V. Simoncini
    The Lyapunov matrix equation. Matrix analysis from a computational perspective
    Quaderno UMI n. 55 - Topics in Mathematics, Bologna - UMI 2015 - pag. 157-174.

  90. Stephen D. Shank , V. Simoncini and Daniel B. Szyld
    Efficient low-rank solutions of Generalized Lyapunov equations
    Numerische Mathematik, 134(2), (2016), 327-342. DOI 10.1007/s00211-015-0777-7

  91. Froilan Dopico , Javier Gonzalez, Daniel Kressner and V. Simoncini
    Projection methods for large T-Sylvester equations
    Mathematics of Computations, v.85, n.301 (2016), pp. 2427--2455. DOI: 10.1090/mcom/3081

  92. Tobias Breiten , V. Simoncini and Martin Stoll
    Fast iterative solvers for fractional differential equations
    Electr. Trans. Numer. Anal., 45 (2016), pp. 107-132.
    The Matlab code is available here

  93. Claudio Canuto , V. Simoncini and Marco Verani
    On the decay of the inverse of matrices that are sum of Kronecker products
    Linear Algebra and its Applications, Volume 452, 1 July 2014, Pages 21-39.

  94. Yiding Lin and V. Simoncini,
    A new subspace iteration method for the algebraic Riccati equation
    Numerical Linear Algebra w/Appl., v.22, n.1, (2015), pp.26-47. DOI: 10.1002/nla.1936

  95. V. Simoncini,
    Computational methods for linear matrix equations (Survey article)
    SIAM Review, 58-3, (2016), pp. 377-441. http://dx.doi.org/10.1137/130912839 (WoS highly cited paper, Jan./Feb. 2019)

  96. S. Shank and V. Simoncini,
    Krylov subspace methods for large scale constrained Sylvester equations
    SIAM. J. Matrix Anal. and Appl. 34-4 (2013), pp. 1448-1463.

  97. V. Simoncini, Daniel B. Szyld and Marlliny Monsalve,
    On two numerical methods for the solution of large-scale algebraic Riccati equations
    IMA Journal of Numerical Analysis, v.34, n.3, (2014), pp.904-920.
  98. Vladimir Druskin, V. Simoncini and Mikhail Zaslavsky,
    Adaptive tangential interpolation in rational Krylov subspaces for MIMO model reduction data
    SIAM J. Matrix Analysis and Appl., v.35, n.2 (2014), 476-498.

  99. Yiding Lin and V. Simoncini,
    Minimal residual methods for large scale Lyapunov equations
    Applied Numerical Mathematics, v.72 (2013), pp.52-71.

  100. Vladimir Druskin, Leonid Knizhnerman and V. Simoncini
    Analysis of the rational Krylov subspace and ADI methods for solving the Lyapunov equation
    SIAM J. Numer. Anal. 49, 2011, pp. 1875-1898.

  101. Tatjana Stykel and V. Simoncini
    Krylov subspace methods for projected Lyapunov equations
    Applied Numerical Mathematics, 62 (2012), pp. 35--50.

  102. V. Druskin and V. Simoncini
    Adaptive rational Krylov subspaces for large-scale dynamical systems
    Systems \& Control Letters, 60 (2011), pp. 546-560.

  103. V. Simoncini and Daniel B. Szyld ,
    On the field of values of oblique projections
    Linear Algebra and its Applications. v.433 n.4, pp. 810-818 (2010).

  104. V. Simoncini and Lars Eldén
    An Error Estimate for the Approximation of $\cosh(\sqrt{A})v$ in the {Krylov} Subspace
    Tech. Rep. LiTH-MAT-R-2010/01--SE, Department of Mathematics, Link\"oping University, Jan 2010. (Report not submitted for publication in a Journal)

  105. Leonid Knizhnerman and V. Simoncini,
    Convergence analysis of the Extended Krylov Subspace Method for the Lyapunov equation
    Numerische Mathematik, Volume 118, Issue 3 (2011), Page 567-586.

  106. Leonid Knizhnerman and V. Simoncini,
    A new investigation of the extended Krylov subspace method for matrix function evaluations
    Numerical Linear Algebra w/Appl. v.17, n.4, pp.615-638 (2010)

  107. Andreas Frommer and V. Simoncini,
    Error bounds for Lanczos approximations of rational functions of matrices
    in ''Numerical Validation", Mathematics in Industry, Lectures Notes in Computer Science, Annie Cuyt and Walter Kr{\"a}mer and Peter Markstein and Wolfram Luther eds, Springer, 2009, v. 5492, pp.203-216.

  108. Lars Eldén and V. Simoncini,
    Solving Ill-Posed Cauchy Problems by a Krylov Subspace Method
    Inverse Problems, v.25, n.6 (June 2009).

  109. V. Simoncini and Vladimir Druskin,
    Convergence analysis of projection methods for the numerical solution of large Lyapunov equations
    SIAM J. Numerical Analysis. Volume 47, Issue 2,pp. 828-843 (2009).


  110. Andreas Frommer and V. Simoncini,
    Stopping criteria for rational matrix functions of Hermitian and symmetric matrices
    SIAM J. Scient. Computing, v.30, n.3 (2008), pp. 1387-1412.

  111. Marina Popolizio and V. Simoncini,
    Acceleration Techniques for Approximating the Matrix Exponential Operator
    SIAM J. Matrix Analysis and Appl. v.30 n.2 (2008), pp.657-683.

  112. V. Simoncini,
    A new iterative method for solving large-scale Lyapunov matrix equations
    SIAM J. Scient. Computing, v.29, n.3 (2007), pp. 1268-1288.

  113. Andreas Frommer and V. Simoncini,
    Matrix functions
    in ``Model Order Reduction: Theory, Research Aspects and Applications'', Mathematics in Industry, Schilders, Wil H. A. and van der Vorst, Henk A. and Rommes, Joost eds, Springer, Heidelberg, 2008, pp.275-304.

  114. Luciano Lopez and V. Simoncini,
    Preserving geometric properties of the exponential matrix by block Krylov subspace methods
    BIT Numerical Mathematics, v. 46, n.4 (2006), pp. 813-830.

  115. Luciano Lopez and V. Simoncini,
    Analysis of projection methods for rational function approximation to the matrix exponential
    SIAM J. Numerical Analysis, v. 44, n. 2 (2006), pp. 613 - 635.

  116. V. Simoncini,
    On the numerical solution of AX-XB=C
    BIT Numerical Mathematics, v. 36 (4) (1996) pp. 814-830.




    Data Science

  117. Domitilla Brandoni, Margherita Porcelli, and V. Simoncini
    A spectral PALM algorithm for matrix and tensor-train based Dictionary Learning
    pp. 1-26, Dipartimento di Matematica, Universita' di Bologna, July 2021. OO E-Print ID : 2021-07-8516, arXiv:12345

  118. Domitilla Brandoni and V. Simoncini
    Tensor-Train Decomposition for image recognition
    Calcolo, v. 57, Article # 9 (2020). DOI: 10.1007/s10092-020-0358-8

    Applications (reverse chronological order)

  119. Alessandro Alla , Dante Kalise, and V. Simoncini
    State-dependent Riccati equation feedback stabilization for nonlinear PDEs
    Adv Comput Math, 49:9, (2023), https://doi.org/10.1007/s10444-022-09998-4

  120. Gerhard Kirsten and V. Simoncini
    A matrix-oriented POD-DEIM algorithm applied to semilinear matrix differential equations
    pp. 1-25, Dipartimento di Matematica, Universita' di Bologna, June 2020. Revised May 2021. arXiv preprint n. 2006.13289 [math.NA].

  121. Alexandra Buenger , V. Simoncini and Martin Stoll
    A low-rank matrix equation method for solving PDE-constrained optimization problems
    SIAM J. Sci. Comput., 43(5), S637-S654, 2021. https://doi.org/10.1137/20M1341210

  122. Yue Hao and V. Simoncini
    Matrix equation solving of PDEs in polygonal domains using conformal mappings
    pp. 1-27, Dipartimento di Matematica, Universita' di Bologna, April 2020. ver 1: HAL archive: hal-02902456.
    To appear in Journal of Numerical Mathematics. DOI: https://doi.org/10.1515/jnma-2020-0035

  123. Maria Chiara D'Autilia, Ivonne Sgura and V. Simoncini
    Matrix-oriented discretization methods for reaction-diffusion PDEs: comparisons and applications
    Computers and Mathematics with Applications, v. 79 (1), 2020, pages 2067-2085. DOI: https://doi.org/10.1016/j.camwa.2019.10.020

  124. C. Arcidiacono and V. Simoncini
    Approximate nonnegative matrix factorization algorithm for the analysis of angular differential imaging data
    Proceedings of SPIE - The International Society for Optical Engineering Volume 10703, 2018, Article number 1070331
    Adaptive Optics Systems VI 2018; Austin; United States; 10 June 2018 through 15 June 2018; Code 139576

  125. Nicola Guglielmi and V. Simoncini
    On the existence and approximation of a dissipating feedback
    pp. 1-23, Dipartimento di Matematica, Universita' di Bologna, October 2018. arXiv: 1811.00069 [math.NA].

  126. Alessandro Alla and V. Simoncini
    Order reduction approaches for the algebraic Riccati equation and the LQR problem
    In: Falcone M., Ferretti R., Grüne L., McEneaney W. (eds) Numerical Methods for Optimal Control Problems.
    Springer INdAM Series, vol 29. Springer, Cham (2018), https://doi.org/10.1007/978-3-030-01959-4_5

  127. Claudio Canuto , V. Simoncini and Marco Verani
    Contraction and optimality properties of an adaptive Legendre-Galerkin method: the multi-dimensional case
    J. Scientific Computing (JOMP), 63(3), (2015), pp 769-798. DOI: 10.1007/s10915-014-9912-3.

  128. M. Zaslavsky, V. Druskin, A. Abubakar, T. Habashy, and V. Simoncini
    Large-scale Gauss-Newton inversion of transient CSEM data using the model reduction framework
    Geophysics, v. 78, n. 4 (July-August 2013); pp. E161–E171.



  129. Vladimir Druskin, V. Simoncini and Mikhail Zaslavsky,
    Solution of the time-domain inverse resistivity problem in the model reduction framework Part I. One-dimensional problem with SISO data
    SIAM J. Scient. Comput., v.35 n.3, (2013) pp. A1621-A1640.

  130. Liliana Ironi, Luigi Panzeri , Erik Plahte and V. Simoncini
    Dynamics of actively regulated gene networks
    Physica D, 240 (2011), pp.779-794.

  131. Michele Benzi, Luis Ferragut, , Micol Pennacchio and V. Simoncini
    Solution of Linear Systems from an Optimal Control Problem Arising in Wind Simulation
    J. Numerical Linear Algebra w/Appl., v. 17, n.6, pp.895-915 (2010).

  132. G. Barbella, F. Perotti and V. Simoncini,
    A numerical procedure for the dynamic response of tall buildings subject to turbulent wind excitation
    Extended abstract, EACWE 5 Florence, Italy 19th – 23rd July 2009.

  133. Micol Pennacchio and V. Simoncini
    Substructuring Preconditioners for the Bidomain Extracellular Potential Problem
    Numerical Mathematics and advanced Applications. Proceedings of ENUMATH 2005, Springer-Verlag (2006), pag. 459-466.

  134. Franco Brezzi , Konstantin Lipnikov , Mikhail Shashkov and V. Simoncini,
    A new discretization methodology for diffusion problems on generalized polyhedral meshes
    Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issues 37-40, 1 August 2007, pp. 3682-3692

  135. Franco Brezzi , Konstantin Lipnikov and V. Simoncini,
    A family of mimetic finite difference methods on polygonal and polyhedral meshes
    M3AS: Mathematical Models and Methods in Applied Sciences, v.15 n.10 (2005) pp. 1533-1552.

  136. F. Perotti and V. Simoncini,
    Analytical and Numerical Techniques in frequency domain response computation
    Recent Research Developments in Structural Dynamics, A. Luongo Ed. Research Signpost Pub., pp. 33-54. 2003.

  137. F. Perotti and V. Simoncini,
    Computational aspects in direct frequency domain analysis
    "Structural Dynamics - EURODYN 2002", Grundmann \& Schueller (eds.) Zwets & Zeitlinger, Lisse (2002), pp. 685-690.

  138. A. Feriani, F. Perotti and V. Simoncini,
    Numerical methods for the performance of direct frequency domain analysis,
    {\it Structural Dynamics} - EURODYN '99,
    L. Fryba and J.Naprstek eds, (1999) Balkema, Rotterdam, pp. 145--150,

  139. A. Feriani, F. Perotti and V. Simoncini,
    Iterative system solvers for the frequency analysis of linear mechanical systems
    Computer Methods in Applied Mech. and Eng., v. 190, n.13-14 (2000) pp. 1719-1739.

  140. G. Erbacci, V. Simoncini, G. Bertero, R. Ansaloni e A. Navarra,
    A spectral finite element model for shallow water equations: implementation experiences on the CRAY T3D, Cray Usergroup Proceedings, Denver, March 1995.

  141. A. Messina, P. Londrillo, L. Moscardini and V. Simoncini
    Numerical experiments on gravitating systems
    IX Italian Conf. on General Rel. and Grav. Physics,
    Cianci et al. eds, pp. 338-352. World Scientific (Singapore), 1991


    Miscellaneous

  142. Stefania Bellavia , Davide Palitta , Margherita Porcelli, and V. Simoncini
    Regularized methods via cubic subspace minimization for nonconvex optimization
    pp. 1-24, June 2023.

  143. Benedetta Morini and V. Simoncini
    Stability and accuracy of Inexact Interior Point methods for convex quadratic programming
    pp.1-23. OO - Optimization Online: 2071/5/6000. To appear in J. of Optimization Theory and Applications

  144. V. Simoncini,
    Krylov Subspaces
    in The Princeton Companion to Applied Mathematics, Sept. 2015.

  145. I. Perugia and V. Simoncini,
    An optimal indefinite preconditioner for a mixed finite element method
    IAN-CNR Tech. Rep. 1098, Nov. 1998.
  146. V. Simoncini,
    Ph.D. Thesis
    (in Italian) Universita' degli Studi di Padova, 1994
  147. V. Simoncini and E. Gallopoulos,
    Iterative methods for complex symmetric systems with multiple right-hand sides
    CSRD Tech. Rep. 1322, Dec. 1993.