# METT VIII - 8th Workshop on Matrix Equations and Tensor Techniques

Nov 6 – 8, 2019
MPI Magdeburg
Europe/Berlin timezone

## A new Riccati ADI method

Nov 7, 2019, 3:00 PM
2h
Main/groundfloor-none - Magistrale (Max Planck Institute for Dynamics of Complex Technical Systems)

200
Poster Posters

### Speaker

Christian Bertram (TU Braunschweig)

### Description

Consider the algebraic Riccati equation
$$A^{*}X + XA + C^*C - XBB^{*}X = 0$$ with large and sparse $A\in \mathbb{C}^{n\times n}$ and $B\in \mathbb{C}^{n\times m}$, $C\in \mathbb{C}^{p\times n}$. The goal is to find an approximate solution $X$ such that the rank of the Riccati residual remains equal to $p$. A method to determine an approximate solution to Riccati equations with this rank property is given by the RADI method [1], a generalization of the ADI method for linear matrix equations. We present a new approach in which solves with $(A^*-\mu I_n)$ and the explicitly known residual factors are sufficient to obtain the unique low-rank residual solution.

[1] Benner, P., Bujanović, Z., Kürschner, P. et al. RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations. Numer. Math. (2018) 138: 301. https://doi.org/10.1007/s00211-017-0907-5

### Primary author

Christian Bertram (TU Braunschweig)

### Co-author

Heike Faßbender (TU Braunschweig)

### Presentation materials

There are no materials yet.