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Showing 1 to 7 of 7 for “"Rational Interpolation"”.
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Rational Interpolation Methods for Nonlinear Eigenvalue Problems
… This observation leads us to explore rational interpolation for system realization, producing a Loewner matrix contour integration technique. The second development of this work studies the application of rational interpolation to the function $T(z)^{-1}$, where we use the poles of …
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Multivariate Rational Approximation in Action: From Data-driven Modeling to Nonlinear Eigenvalue Problems
… presented results are related to multivariate rational approximation methods, in particular the parametric adaptive Antoulas–Anderson (p-AAA) algorithm. The algorithm is inspired by the adaptive Antoulas-Anderson (AAA) algorithm for univariate rational approximation and combines rational …
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Krylov Projection Methods for Model Reduction
… lead to a class of reduced-order models known as rational interpolants. The cornerstone of this dissertation is a collection of theory relating Krylov projection to rational interpolation. Based on this theoretical framework, three algorithms for model reduction are proposed. The first algorithm, …
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On Vector Sequence Transforms and Acceleration Techniques
… to accelerations based upon generalizations of rational interpolation and Pade approximation. Further acceleration techniques using Sherman-Woodbury-Morrison type formulas are formulated and suggested as a replacement for the E-transform.</p> <p>We contrast the effect of several extrapolation …
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An Interpolation-Based Approach to Optimal H<sub>∞</sub> Model Reduction
… model reduction problem broadly from an interpolation-based approach, and give a method for finding the approximation to a state-space symmetric dynamical system which is optimal over a family of interpolants to the full order system. This family of interpolants has a simple …
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Efficient 𝐻₂-Based Parametric Model Reduction via Greedy Search
Dynamical systems are mathematical models of physical phenomena widely used throughout the world today. When a dynamical system is too large to effectively use, we turn to model reduction to obtain a smaller dynamical system that preserves the behavior of the original. In many cases these models …
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Dimension Reduction in Structured Dynamical Systems: Optimal-𝓗<sub>2</sub> Approximation, Data-Driven Balancing, and Real-Time Monitoring
… the Sylvester equation-based (Wilson) and interpolation-based (Meier-Luenberger) $mathcal{H}_2$-optimality frameworks for this class of systems. These frameworks are based on two independent sets of first-order necessary conditions for optimality. We additionally show how to enforce the …