Most of the software under current development is hosted on the page of the NumPI group on Github.

## Numerical libraries and tools

- CQT Toolbox: A toolbox for MATLAB implementing the arithmetic of finite and semi-infinite quasi-Toeplitz matrices (i.e., Toeplitz + low-rank corrections).

- HM Toolbox: A toolbox for MATLAB implementing HODLR and HSS rank-structured arithmetic. The toolbox is under active development (especially the HSS part).

- MPSolve 3: The new version of the MPSolve package for polynomial root approximation.

- MPSolve 2.2: The older version of MPSolve, was released in 2001.

- PGDoubling: A MATLAB package to solve algebraic Riccati equations and optimal control problems using permuted graph bases.

- PSCToolkit: A suite of software for distributed sparse linear algebra (Krylov solvers and AMG preconditioners). It runs on hundreds of thousands of CPUs and thousand of GPUs, and is an Excellent Science INNOVATION in the EU Innovation Radar.

- SMCSolver: A software tool to solve some classes of Markov Chains frequently encountered in queuing models.

## Scripts and numerical experiments

- Rank Structured Hessenberg Reduction: A MATLAB toolbox implementing the rank structured Hessenberg reduction presented in the paper “Fast Hessenberg reduction of some rank structured matrices”, by L. Gemignani and L. Robol.

- Secular linearization: Some Matlab scripts to reproduce the experiments in the paper “On a class of matrix pencils equivalent to a given matrix polynomial”.

- StarSylv: A FORTRAN implementation of the solver for a system of $\top$-Sylvester equations described in the paper “Nonsingular systems of generalized Sylvester equations: an algorithmic approach”, by F. De Terán, B. Iannazzo, F. Poloni, L. Robol.

- SQT: Quasi-Toeplitz matrices with a symmetric symbol. Software from the paper “On certain matrix algebras related to quasi-Toeplitz matrices”, by D.A. Bini and B. Meini.
- MGM: Matrix Geometric Mean. Software from the paper “Computational aspects of the geometric mean of two matrices: a survey” by D.A. Bini and B. Iannazzo.