Recent Updates in Two Competitive Algorithms for Model Reduction of Large-Scale Dynamical Systems

Mohammed Nizam Uddin; Mohammad Monir Uddin; Muhammad Hanif

doi:https://doi.org/10.14445/22315373/IJMTT-V57P555

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 57 | Number 6 | Year 2018 | Article Id. IJMTT-V57P555 | DOI : https://doi.org/10.14445/22315373/IJMTT-V57P555

Recent Updates in Two Competitive Algorithms for Model Reduction of Large-Scale Dynamical Systems

Mohammed Nizam Uddin, Mohammad Monir Uddin, Muhammad Hanif

Citation :

Mohammed Nizam Uddin, Mohammad Monir Uddin, Muhammad Hanif, "Recent Updates in Two Competitive Algorithms for Model Reduction of Large-Scale Dynamical Systems," International Journal of Mathematics Trends and Technology (IJMTT), vol. 57, no. 6, pp. 402-407, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V57P555

Abstract

The modern approach, to explore scientific ideas to convince others of their validations, is through computer simulations. In simulation, one needs to convert a physical model into a mathematical model. Often also in real-life applications the mathematical models are represented by linear time-invariant (LTI) continuous-time systems. A large system leads to additional memory requirements and enormous computational efforts. Therefore,reducing the size of the system is an indispensable task for fast simulations. Various techniques are proposed in the literature to reduce the size of the large-scale LTI continuous-time systems. Among those, the Gramian based method Balanced truncation (BT) and interpolatoryprojection based method Iterative rational Krylov algorithm (IRKA) are most commonly used techniques. This article shows the comparisons between the BT andIRKA using their recent developments.

Keywords

LTI continuous-time system, model reduction,balanced truncation, iterative rational Krylov algorithm.

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