5 papers · 1 filter
Wavelet-Based Observables for Koopman Analysis: An Extended Dynamic Mode Decomposition Framework
Cankat Tilki, Serkan Gugercin
We present an in-depth analysis of the Koopman semigroup via wavelet transform. Towards this goal, we start by introducing the wavelet-based observables and show that they are eige…
A refined nonlinear least-squares method for the rational approximation problem
Michael S. Ackermann, Linus Balicki, Serkan Gugercin +1
The adaptive Antoulas-Anderson (AAA) algorithm for rational approximation is a widely used method for the efficient construction of highly accurate rational approximations to given…
A parametric Keldysh decomposition
Linus Balicki, Mark Embree, Serkan Gugercin
Contour integral algorithms seek to compute a small number of eigenvalues located within a bounded region of the complex plane. These methods can be applied to both linear and nonl…
Multivariate Rational Approximation of Scattered Data Using the p-AAA Algorithm
Linus Balicki, Serkan Gugercin
Many algorithms for approximating data with rational functions are built on interpolation or least-squares approximation. Inspired by the adaptive Antoulas-Anderson (AAA) algorithm…
Multivariate Rational Approximation via Low-Rank Tensors and the p-AAA Algorithm
Linus Balicki, Serkan Gugercin
Approximations based on rational functions are widely used in various applications across computational science and engineering. For univariate functions, the adaptive Antoulas-And…