Valeria Simoncini

Available software



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  • EVEN_IRA

    This Matlab code is available here

    Related article:
    Volker Mehrmann , Christian Schroeder and V. Simoncini
    An Implicitly-restarted Krylov Method for Real Symmetric/Skew-Symmetric Eigenproblems
    Linear Algebra and Appl., 436 (10), (2012), pp. 4070-4087.

  • KPIK

    This Matlab code approximately solves a large-scale Lyapunov matrix equation by means of the
    Extended Krylov method with Galerkin condition. Version 1.0. Download kpik.m
    Here is an example of how to call the function kpik.m. Download example_kpik.m
    The code does not include any checking of the input data.

    Related article:
    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.
  • KPIK_SYLV

    This Matlab code approximately solves a large-scale Sylvester matrix equation by means of the
    Extended Krylov method with Galerkin condition. Version 1.0. Download kpik_sylv.m
    Here is an example of how to call the function kpik_sylv.m. Download example_kpik_sylv.m
    The code does not include any checking of the input data.
    Deflated version to be included.

    Related article:
    T. Breiten , V. Simoncini and M. Stoll
    Fast iterative solvers for fractional differential equations
    pp.1-32, January 2014. To appear in ETNA.

  • RKSM for Lyapunov equations

    This Matlab code approximately solves a large-scale Lyapunov matrix equation by means of the
    adaptive Rational Krylov method with Galerkin condition. Version 1.0. Download rksm.m
    Here is an example of how to call the function rksm.m. Download example_rksm.m
    The code does not include any checking of the input data.

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


  • Tangential RKSM for Lyapunov equations

    This Matlab code approximately solves a large-scale Lyapunov matrix equation by means of the
    adaptive Rational Krylov method with Galerkin condition.
    A tangential approach is used to deal with large rank of the known ``rhs'' matrix BB'.
    Version 1.0. Download rksm_tan_lyap_amg_Mdir.m
    Here is an example of how to call the function rksm.m. Download example_rksm_tan.m
    The code does not include any checking of the input data.

    Related article:
    V. Druskin, V. Simoncini and M. 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.


  • Iterative solver for generalized Lyapunov equations

    This Matlab code approximately solves a generalized (multiterm) large-scale Lyapunov matrix equation by means
    of a splitting iterative method. At each iteration, the algorithm solves
    a Lyapunov equation with the extended Krylov method with Galerkin condition.
    Version 1.0. Download efficientGenLyap.m , Download EKS.m , Download invertA.m ,
    Here is an example of how to call the function efficientGenLyap.m. Download example_Glyap.m
    The code does not include any checking of the input data.

    Related article:
    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



  • SKSM_cTri: Enhanced standard Krylov subspace method for symmetric Lyapunov equations

    This Matlab code iteratively solves a large-scale Lyapunov matrix equation with symmetric coeff. matrix by means of the
    standard Krylov method with Galerkin condition (low CPU and memory requirements). Version 1.0.
    Download: SKSM_cTri.m , cTri.mexa64
    Here is an example of how to call the function SKSM_cTri.m. Download example_SKSM_cTri.m
    The code does not include any checking of the input data.

    Related manuscript:
    Davide Palitta and V. Simoncini,
    Computationally enhanced projection methods for symmetric Sylvester and Lyapunov matrix equations
    ArXiv: 1602.05033 . February 2016.



  • RKSM for Riccati equations

    This Matlab code approximately solves a large-scale Riccati matrix equation by means of the
    adaptive Rational Krylov method with Galerkin condition. Version 1.0. Download ARKSM_Riccati.m
    Here is an example of how to call the function rksm.m. Download test_ARKSM_Riccati.m
    The code does not include any checking of the input data.

    Related article:
    V. Simoncini,
    Analysis of the rational Krylov subspace projection method for large-scale algebraic Riccati equations
    arxiv 1602.00649 [math.NA]. January 2016.


  • MR_RKSM

    (to be included)