14 citations · 40 across the 24 of their papers we have counts for
27 papers
Numerical Solution of Large-Scale Low-Rank Coupled Generalized Sylvester Equations
Umair Zulfiqar
This paper develops projection methods for computing low-rank solutions to large-scale coupled generalized Sylvester equations. The dominant subspaces of these solutions are shown…
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…
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…
From Data to Balanced Truncation Family: A Projection-based Non-intrusive Approach
Umair Zulfiqar
This paper presents data-driven implementations of balanced truncation and several of its generalizations that rely exclusively on transfer function samples on the imaginary axis.…
A Unified Low-rank ADI Framework with Shared Linear Solves for Simultaneously Solving Multiple Lyapunov, Sylvester, and Riccati Equations
Umair Zulfiqar, Zhong-Yi Huang, Qiu-Yan Song +1
The alternating direction implicit (ADI) methods are computationally efficient and numerically effective tools for computing low-rank solutions of large-scale linear matrix equatio…
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…
Non-intrusive Data-driven ADI-based Low-rank Balanced Truncation
Umair Zulfiqar
In this short note, a non-intrusive data-driven formulation of ADI-based low-rank balanced truncation is provided. The proposed algorithm only requires transfer function samples at…
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…
Balanced Truncation via Tangential Interpolation
Umair Zulfiqar, Zhi-Hua Xiao, Qiu-yan Song +1
This paper examines the construction of rth-order truncated balanced realizations via tangential interpolation at r specified interpolation points. It is demonstrated that when the…
Data-driven H2-optimal Model Reduction via Offline Transfer Function Sampling
Umair Zulfiqar
-optimal model order reduction algorithms represent a significant class of techniques, known for their accuracy, which has been extensively validated over the past t…
Time-limited H2-optimal Model Order Reduction of Linear Systems with Quadratic Outputs
Umair Zulfiqar, Zhi-Hua Xiao, Qiu-Yan Song +2
An important class of dynamical systems with several practical applications is linear systems with quadratic outputs. These models have the same state equation as standard linear t…
-optimal Model Reduction of Linear Quadratic Output Systems in Finite Frequency Range
Umair Zulfiqar, Zhi-Hua Xiao, Qiu-Yan Song +2
In frequency-limited model order reduction, the objective is to maintain the frequency response of the original system within a specified frequency range in the reduced-order model…
Balanced Truncation of Linear Systems with Quadratic Outputs in Limited Time and Frequency Intervals
Qiu-Yan Song, Umair Zulfiqar, Zhi-Hua Xiao +2
Model order reduction involves constructing a reduced-order approximation of a high-order model while retaining its essential characteristics. This reduced-order model serves as a…
Relative Error-based Time-limited H2 Model Order Reduction via Oblique Projection
Umair Zulfiqar, Xin Du, Qiuyan Song +2
In time-limited model order reduction, a reduced-order approximation of the original high-order model is obtained that accurately approximates the original model within the desired…
Frequency-limited H Model Order Reduction Based on Relative Error
Umair Zulfiqar, Xin Du, Qiuyan Song +2
Frequency-limited model order reduction aims to approximate a high-order model with a reduced-order model that maintains high fidelity within a specific frequency range. Beyond thi…
On frequency- and time-limited H2-optimal model order reduction
Umair Zulfiqar, Victor Sreeram, Xin Du
In this paper, the problems of frequency-limited and time-limited H2-optimal model order reduction of linear time-invariant systems are considered within the oblique projection fra…
Frequency-weighted H2-optimal model order reduction via oblique projection
Umair Zulfiqar, Victor Sreeram, Mian Ilyas Ahmad +1
In projection-based model order reduction, a reduced-order approximation of the original full-order system is obtained by projecting it onto a reduced subspace that contains its do…
Time- and frequency-limited H2-optimal model order reduction of bilinear control systems
Umair Zulfiqar, Victor Sreeram, Mian Ilyas Ahmad +1
In the time- and frequency-limited model order reduction, a reduced-order approximation of the original high-order model is sought to ensure superior accuracy in some desired time…
Adaptive Frequency-limited H2-Model Order Reduction
Umair Zulfiqar, Victor Sreeram, Xin Du
In this paper, we present an adaptive framework for constructing a pseudo-optimal reduced model for the frequency-limited H2-optimal model order reduction problem. We show that the…