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Shuai Shao (The University of Manchester)5/19/26, 2:00 PMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
We propose an asympotically optimal choice of shared concentrated real poles of a family of rational approximants of time-dependent exponential functions exp(−𝑡𝑧) for 𝑧 ≥ 0 and 𝑡 in a positive time interval 𝑇. Our result extends a classical result by J.-E. Andersson [J. Approx. Theory, 32(2):85–95, 1981] on the asymptotic best rational approximation of exp(−𝑧) with real poles. Numerical...
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Linus Balicki (Novateur Research Solutions)5/19/26, 2:25 PMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
The parametric adaptive Antoulas–Anderson (p-AAA) algorithm is an effective method for multivariate rational approximation [Carracedo Rodriguez et al., 2023], inspired by the AAA framework for univariate rational approximation [Nakatsukasa et al., 2018].
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In its original formulation, p-AAA aims to approximate a function $\mathbf{f} : \mathbb{C}^d \rightarrow \mathbb{C}$ via a multivariate... -
Karl Meerbergen (KU Leuven)5/19/26, 2:50 PMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
We present an extension of the AAA algorithm, named psvAAA. This MOR method combines the multivariate pAAA and uni-variate set valued AAA method. Many physical systems are described by dynamical systems with physical or geometrical parameters. Often, the system's output is strongly dependent on the Laplace variable or the frequency, and less strong on the parameters. In this talks, we present...
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Michael Ackermann (Virginia Tech)5/20/26, 10:45 AMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
The adaptive Anderson-Antoulas (AAA) algorithm is capable of generating highly accurate rational approximations to given data. Though AAA almost always produces an approximation to a given target accuracy, the degree of the resulting rational function may be larger than actually required to meet the accuracy tolerance. In this talk, we introduce the nonlinear least-squares adaptive...
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Athanasios Antoulas (Rice University)5/20/26, 11:10 AMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
Purpose of this presentation is to discuss novel descriptor realizations of linear multiple-parameter systems and their connection to nonlinear eigenvalue problems. The work is based on recent developments of the Loewner framework as exposed in a SIAM Review paper, published in November 2025.
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Sean Reiter (Courant Institute of Mathematical Sciences, New York University)5/20/26, 11:35 AMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
In recent years, structured reduced-order modeling has become an essential component in meaningful applications across engineering and the physical sciences whenever mathematical models are unavailable, but input-output data are abundant. For linear time-invariant systems, the Loewner framework provides a non-intrusive methodology for the construction of minimal interpolants from rational...
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Luka Marohnić (Zagreb University of Applied Sciences)5/21/26, 11:00 AMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
We introduce an AAA-type method for rational quasi-Hermite approximation formulated in barycentric form. A stacked Hermite–Löwner matrix is assembled from function values and derivative data at adaptively selected support nodes, and the barycentric weights are determined through a homogeneous least-squares procedure. This approach eliminates the need for external test points as required in the...
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Leonie Van Pottelberghe (KU Leuven)5/21/26, 11:25 AMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
Recent contributions for rational approximation include the p-AAA method (and variations) and the extension of the Loewner framework to multiple dimensions. These contributions are recent and are inspiration for further analysis and algorithmic improvements.
In this talk, we combine two ingredients that have proven to be successful in their respective contexts, i.e., the AAA method for...
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Akil Narayan (University of Utah)5/21/26, 11:50 AMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
We discuss analytical estimates for greedy construction of rational approximations, where the underlying function is the linear sketch of an operator resolvent. The canonical example of this setup is the transfer function of a linear dynamical system. Under a sectorial assumption for the operator, this analysis immediately reveals corresponding algorithms, and provides explicit estimates of...
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