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M-M.E.S.S. - The Matrix Equation Sparse Solver Library

Abstract

The M-M.E.S.S. toolbox provides solvers for large-scale, sparse, symmetric linear and quadratic matrix equations. These can be algebraic and differential equations and the solvers are in their core all based on the low-rank ADI method. M-M.E.S.S. can be seen as the successor to the LyaPack toolbox with an improved formulation of the ADI, that now properly supports generalized state space systems, but also special structured DAEs. It features additional solvers for differential equations, improved shift parameter computation and a guarantee to compute real low-rank factorizations, but follows the same general philosophy of user supplied functions that the LyaPack toolbox used.

The Software is provided as a Matlab toolbox (mltbx) file, an Octave package (tar.gz) and a zip-archive. The toolbox-file needs a recent Matlab version to install properly. The Octave package was tested in Octave 4.0 and above. The content of the zip-archive is equipped with all functions to also run on older releases. In order to get all functions registered properly, change to the installation folder and run the mess_path function. This will set the searchpath correctly for the current session.

Keywords

Splitting Methods, RADI, Low-Rank Alternating Directions Implicit, Lyapunov equation, Nonautonomous DREs, Linear Quadratic Regulator, Lyapunov Equation, Riccati equation, Riccati Iteration, sparse-dense Sylvester Equations, Riccati Equation, MESS, Model Order Reduction, Balanced Truncation, Newton Kleinman Iteration, IRKA, Rosenbrock Method, Backward Differentiation Formula, Lyapunov-plus-positive Equations, http://www.ams.org/mathscinet/msc/msc2010.html

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
views
OpenAIRE UsageCountsViews provided by UsageCounts
downloads
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20
Top 10%
Top 10%
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106
10