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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.

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.

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.

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.

T. Breiten , V. Simoncini and M. Stoll

Fast iterative solvers for fractional differential equations

pp.1-32, January 2014. To appear in ETNA.

adaptive Rational Krylov method with Galerkin condition.

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.

Here is an example of how to call the function RKSM_Lyap_real.m. Download example_lyap_real.m

The code does not include any checking of the input data.

V. Druskin and V. Simoncini,

Adaptive rational Krylov subspaces for large-scale dynamical systems

Systems & Control Letters, 60 (2011), pp. 546-560.

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.

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.

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.

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

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.

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.

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.

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

adaptive Rational Krylov method with Galerkin condition (MOR style: projecting and then time-integrating) Version 1.2.

Download DRE.tar.gz

The code does not include any checking of the input data. See also here for the GitHub version.

Gerhard Kirsten and V. Simoncini,

Order reduction methods for solving large-scale differential matrix Riccati equations

To appear in SIAM J. Scient. Comput. arXiv: 1905.12119. https://arxiv.org/abs/1905.12119

Download here .

The code does not include any checking of the input data.

Davide Palitta and V. Simoncini

Numerical methods for large-scale Lyapunov equations with symmetric banded data

SIAM J. Scientific Computing. v.40 (5), pp.A3581--A3608 (2018). https://doi.org/10.1137/17M1156575

Version 1.0.

Download: MultiRB.zip .

The package contains the driver SGFEM_matdriver.m to replicate the examples in the related article.

The code does not include any checking of the input data.

C.E. Powell, D. Silvester, V. Simoncini,

An Efficient Reduced Basis Solver for Stochastic Galerkin Matrix Equations,

SIAM J. Sci. Comput., Vol 39, No. 1, pp. A141--A163, (2017)