14 citations · 16 across the 18 of their papers we have counts for
26 papers
A Low-rank ADI Algorithm for the Numerical Solution of Large Discrete-time Non-symmetric Algebraic Riccati Equations
Umair Zulfiqar
Discrete-time non-symmetric algebraic Riccati equations (DTNAREs) arise in game-theoretic computations of Nash equilibria. Solving such equations at large scale is often computatio…
D-RADI: A Low-rank ADI Algorithm for Solving Large-scale Discrete-time Algebraic Riccati Equations
Umair Zulfiqar
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…
A New Generalized Low-Rank Cholesky Factor ADI Algorithm for Large-Scale Stein Equations
Umair Zulfiqar
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…
A New Low-Rank Cholesky-Factor ADI Algorithm Allowing Shifts Anywhere in the Complex Plane with Applications to Data-Driven Model Reduction
Umair Zulfiqar
The low-rank Cholesky factor alternating direction implicit (LRCF-ADI) iteration method is an effective and efficient approach for computing low-rank solutions to large-scale Lyapu…
A Low-rank Interpolatory Projection Algorithm for Solving Large-scale T-Sylvester Equations
Umair Zulfiqar
This paper considers large-scale T-Sylvester equations of the form , which admit a low-rank solution. It is shown that when the unique solutio…
A Low-rank ADI Algorithm for Solving Large-scale Non-symmetric Algebraic Riccati Equations
Umair Zulfiqar
This paper considers large-scale nonsymmetric continuous-time algebraic Riccati equations (NAREs) that admit low-rank solutions. Low-rank alternating direction implicit (ADI) metho…