%0 Book Section %1 demarchi2017rescaled %A De Marchi, Stefano %A Idda, Andrea %A Santin, Gabriele %B Approximation Theory XV: San Antonio 2016 %C Cham %D 2017 %E Fasshauer, Gregory E. %E Schumaker, Larry L. %I Springer International Publishing %K imported vorlaeufig %P 39--59 %R 10.1007/978-3-319-59912-0_3 %T A Rescaled Method for RBF Approximation %U https://doi.org/10.1007/978-3-319-59912-0_3 %X In the recent paper 1, a new method to compute stable kernel-based interpolants has been presented. This rescaled interpolation method combines the standard kernel interpolation with a properly defined rescaling operation, which smooths the oscillations of the interpolant. Although promising, this procedure lacks a systematic theoretical investigation. Through our analysis, this novel method can be understood as standard kernel interpolation by means of a properly rescaled kernel. This point of view allows us to consider its error and stability properties. %@ 978-3-319-59912-0

@inbook{demarchi2017rescaled, abstract = {In the recent paper [1], a new method to compute stable kernel-based interpolants has been presented. This rescaled interpolation method combines the standard kernel interpolation with a properly defined rescaling operation, which smooths the oscillations of the interpolant. Although promising, this procedure lacks a systematic theoretical investigation. Through our analysis, this novel method can be understood as standard kernel interpolation by means of a properly rescaled kernel. This point of view allows us to consider its error and stability properties.}, added-at = {2018-07-20T10:54:15.000+0200}, address = {Cham}, author = {De Marchi, Stefano and Idda, Andrea and Santin, Gabriele}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2457ee4d0e4349fe956682f44cc20759f/mhartmann}, booktitle = {Approximation Theory XV: San Antonio 2016}, doi = {10.1007/978-3-319-59912-0_3}, editor = {Fasshauer, Gregory E. and Schumaker, Larry L.}, interhash = {f31e4e68f9384a84cbddbdf77cbc5ea6}, intrahash = {457ee4d0e4349fe956682f44cc20759f}, isbn = {978-3-319-59912-0}, keywords = {imported vorlaeufig}, owner = {santinge}, pages = {39--59}, publisher = {Springer International Publishing}, timestamp = {2018-07-20T08:54:15.000+0200}, title = {A Rescaled Method for {RBF} Approximation}, url = {https://doi.org/10.1007/978-3-319-59912-0_3}, year = 2017 }