Speaker
Description
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 classical AAA algorithm. To maintain computational efficiency, the barycentric weights are computed using randomized nullspace methods, which accelerate the SVD of the stacked Hermite–Löwner matrices.
To further control computational costs and mitigate the appearance of spurious poles, the support set is adaptively partitioned into pieces. This yields piecewise rational quasi-Hermite approximants where inter-piece smoothness is enforced through penalization rather than exact spline constraints, significantly reducing the size of the underlying SVD problems and suppressing unwanted poles. The refinement strategy estimates the location of the maximal residual by constructing a Hermite interpolant of the residual data over the current support nodes. A complete MATLAB implementation is provided, and numerical experiments demonstrate that the method achieves accuracy and efficiency comparable to continuum AAA while requiring substantially fewer function evaluations when derivative information is available.