Matrix Equation Sparse Solvers (MESS): A MATLAB Toolbox for the Solution of Sparse Large-Scale Matrix Equations. MESS is the successor to the LyaPack Toolbox for MATLAB. It is intended for solving large sparse matrix equations. The new version has been rewriten in large parts to fit the drastic upgrades in the Matlab releases since 2000. Additionally new solvers for differential Riccati equations extend the functionality and many enhancements upgrade the efficiency and runtime behaviour enlarging the number of unknowns that can now be computed. Amongst other things, it can solve Lyapunov and Riccati equations, and do model reduction. Even though MESS has been implemented in MATLAB rather than programming languages like FORTRAN, C, or JAVA, this does not mean that MESS is restricted to the solution of”toy problems”. Several measures, such as the use of global variables for large data structures, have been taken to enhance the computational performance of MESS routines. To put this into the right perspective, Lyapunov equations of order 20000 were solved by MESS within few minutes on a regular laptop computer. On a 64bit computeserver algebraic Riccati equations of order 250 000 have been solved in less than 1 day. When using standard (dense) methods, supercomputers are needed to solve problems of this size.
Keywords for this software
References in zbMATH (referenced in 5 articles )
Showing results 1 to 5 of 5.
- Fan, Hung-Yuan; Weng, Peter Chang-Yi; Chu, Eric King-Wah: Numerical solution to generalized Lyapunov/Stein and rational Riccati equations in stochastic control (2016)
- Chu, Eric King-wah; Weng, Peter Chang-Yi: Large-scale discrete-time algebraic Riccati equations -- doubling algorithm and error analysis (2015)
- Li, Tiexiang; Chu, Eric King-Wah; Lin, Wen-Wei; Weng, Peter Chang-Yi: Solving large-scale continuous-time algebraic Riccati equations by doubling (2013)
- Li, Tiexiang; Weng, Peter Chang-Yi; Chu, Eric King-wah; Lin, Wen-Wei: Large-scale Stein and Lyapunov equations, Smith method, and applications (2013)
- Bini, Dario A.; Iannazzo, Bruno; Meini, Beatrice: Numerical solution of algebraic Riccati equations. (2012)