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On a Recovery Problem
(1995)SAM Research ReportThis paper concerns itself with the recovery of the coefficients, shifts and, where applicable, dilates of a given form f(\bfx)=∑j=1mcjG(\bfx−\bftj), or f(\bfx)=∑j=1mcjg(\bfaj⋅\bfx−bj),\bfx∈\RRn, where emf/em, emG/em and emg/em are known. That is, we provide a method that identifies the quantities $c_j$, $\bft_j$, $\bfa_j$ and $b_j$. In some cases we can even find emG/em given only emf/em and knowing that emf/em is of the above form.Report -
Radial Functions on Compact Support
(1995)SAM Research ReportIn this paper, radial basis functions that are compactly supported and give rise to positive definite interpolation matrices for scattered data are discussed. They are related to the well-known thin plate spline radial functions which are highly useful in applications for gridfree approximation methods. Also, encouraging approximation results for the compactly supported radial functions are shown.Report -
Neue und alte Thesen über Wavelets
(1995)SAM Research ReportIn diesem Artikel soll eine erste, kurze Einfuehrung in die Theorie der Wavelets gegeben werden, die ohne besondere Vorkenntnisse zugaenglich ist. Anhand einiger Beispiele werden insbesondere die Zielsetzungen, die mit der Waveletanalyse verfolgt werden, erlaeutert, so beispielsweise die Kompression grosser Datenmengen oder die Suche nach gegebenen Mustern oder Singularitaeten. Die besonderen Eigenschaften der Waveletanalyse, die sie von ...Report -
Spectral Properties and Knot removal for Interpolation by Pure Radial Sums
(1995)SAM Research ReportWe investigate some asymptotic spectral properties of the collocation matrix arising in interpolation by pure radial sums, and we provide some theoretical results that can be used for knot removal.Report