.png){kind=icon}
Return
RATIONAL KERNEL-BASED INTERPOLATION FOR COMPLEX-VALUED FREQUENCY RESPONSE FUNCTIONS]
.png){kind=icon}
OA
AI
DOI：10.1137/23M1588901.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the response function of a partial differential equation in the frequency domain is of particular interest. In this setting, kernel methods are employed more and more frequently; however, standard kernels do not perform well. Moreover, the role and mathematical implications of the underlying pair of kernels, which arise naturally in the complex-valued case, remain to be addressed. We introduce new reproducing kernel Hilbert spaces of complex-valued functions and formulate the problem of complex-valued interpolation with a kernel pair as minimum-norm interpolation in these spaces. Moreover, we combine the interpolant with a low-order rational function, where the order is adaptively selected based on a new model selection criterion. Numerical results on examples from different fields, including electromagnetics and acoustics examples, illustrate the performance of the method in comparison to available rational approximation methods.
Keywords:
complex-valued kernel methods
dynamical systems
frequency response function
model selection
rational approximation
Journal
IF:
2.6
Papers:
5.1K
Citations:
1.8W
Organization
View more organizations
Cited Papers
.png){kind=icon}
ShareSaveShareSaveA remark on the Gaussian lower bound for the Neumann heat kernel of the Laplace–Beltrami operator
OAAI
OAAIShareSaveShareSaveShareSaveShareSave View more