11 papers
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…
Factorization-based Generalized Low-rank ADI Algorithm for Solving Large-scale Algebraic Riccati Equations
Umair Zulfiqar
The low-rank alternating direction implicit (ADI) method is an efficient and effective solver for large-scale standard continuous-time algebraic Riccati equations that admit low-ra…
Data-driven Implementations of Various Generalizations of Balanced Truncation
Umair Zulfiqar, Qiu-Yan Song, Zhi-Hua Xiao +1
Quadrature-based approximation of Gramians in standard balanced truncation yields a non-intrusive, data-driven implementation that requires only transfer function samples on the im…
Compression and Distillation of Data Quadruplets in Non-intrusive Reduced-order Modeling
Umair Zulfiqar
This paper introduces a quadrature-free, non-intrusive approach to balanced truncation for both continuous-time and discrete-time systems. The method non-intrusively constructs red…