Author

Umair Zulfiqar

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Preprint Aug 2026

D-RADI: A Low-rank ADI Algorithm for Solving Large-scale Discrete-time Algebraic Riccati Equations

The low-rank alternating direction implicit (ADI) method is an efficient numerical technique for solving several types of large-scale matrix equations that admit low-rank solutions. The discrete-time algebraic Riccati equation (DARE) is an important matrix equation with applications in state estimation, controller desi...

Umair Zulfiqar · 0 citations

Preprint Sep 2026

A Low-rank ADI Algorithm for the Numerical Solution of Large Discrete-time Non-symmetric Algebraic Riccati Equations

Discrete-time non-symmetric algebraic Riccati equations (DTNAREs) arise in game-theoretic computations of Nash equilibria. Solving such equations at large scale is often computationally prohibitive. This paper develops a numerical approach for large-scale DTNAREs whose solutions are low rank. A low-rank alternating dir...

Umair Zulfiqar · 0 citations

Preprint Aug 2026

A New Generalized Low-Rank Cholesky Factor ADI Algorithm for Large-Scale Stein Equations

The low-rank alternating direction implicit (ADI) method is an efficient solver for large-scale Stein equations with low-rank solutions. This paper shows that, as in the continuous-time Lyapunov equation case, the low-rank Cholesky factor ADI (LRCF-ADI) method for Stein equations implicitly performs $\mathcal{H}_2$-pse...

Umair Zulfiqar · 2 citations · ⚡1