We hope this content on epidemiology, disease modeling, pandemics and vaccines will help in the rapid fight against this global problem. Click on title above or here to access this collection. Mathematical models are used to simulate, and sometimes control, the behavior of physical and artificial processes such as the weather and very large-scale integration VLSI circuits. The increasing need for accuracy has led to the development of highly complex models. However, in the presence of limited computational, accuracy, and storage capabilities, model reduction system approximation is often necessary. Approximation of Large-Scale Dynamical Systems provides a comprehensive picture of model reduction, combining system theory with numerical linear algebra and computational considerations.
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Large scale dynamical systems are a common framework for the modeling and control of many complex phenomena of scientific interest and industrial value, with examples of diverse origin that include signal propagation and interference in electric circuits, storm surge prediction before an advancing hurricane, vibration suppression in large structures, temperature control in various media, neurotransmission in the nervous system, and behavior of micro-electro-mechanical systems.
Direct numerical simulation of underlying mathematical models is one of few available means for accurate prediction and control of these complex phenomena. The need for ever greater accuracy compels inclusion of greater detail in the model and potential coupling to other complex systems leading inevitably to very large-scale and complex dynamical models.
Simulations in such large-scale settings can make untenable demands on computational resources and efficient model utilization becomes necessary. Model reduction is one response to this challenge, wherein one seeks a simpler typically lower order model that nearly replicates the behavior of the original model.
When high fidelity is achieved with a reduced-order model, it can then be used reliably as an efficient surrogate to the original, perhaps replacing it as a component in larger simulations or in allied contexts such as development of simpler, faster controllers suitable for real time applications.
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Interpolatory Model Reduction of Large-Scale Dynamical Systems
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Approximation of Large-Scale Dynamical Systems