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    • 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:

D. Palitta and Valeria Simoncini, Computationally enhanced projection methods for symmetric Sylvester and Lyapunov matrix equations.


    • EKSM_genSylv_LRcomm: Extended Krylov Subspace Method for generalized Sylvester equations with low-rank commuting coefficients

This Matlab code iteratively solves large-scale generalized Sylvester and Lyapunov matrix equations with low-rank commuting coefficients by means of the extended Krylov method and a proper selection of the starting blocks. Version 1.0.

Download: EKSM_genSylv_LRcomm.m, EKSM_genLyap_LRcomm.m, GenSylv_smallscale.m

Here are two examples of how to call the functions EKSM_genSylv_LRcomm.m and EKSM_genLyap_LRcomm.m respectively. Download Inhomogeneus_Helmholtzeq.m, MIMO_example.m.

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

Related manuscript:

Elias Jarlebring, Giampaolo Mele, D. Palitta and Emil Ringh, Krylov methods for low-rank commuting generalized Sylvester equations.


  • hm-toolbox: Matlab Toolbox implementing H-matrices arithmetic. It includes routines for solving large-scale Lyapunov and Sylvester matrix equations with quasiseparable data.

Related manuscript:

Stefano Massei, D.P. and Leonardo Robol, Solving rank structured Sylvester and Lyapunov equations.