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Computer Science > Numerical Analysis

arXiv:cs/0207062 (cs)
[Submitted on 15 Jul 2002]

Title:Some addenda on distance function wavelets

Authors:W. Chen
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Abstract: This report will add some supplements to the recently finished report series on the distance function wavelets (DFW). First, we define the general distance in terms of the Riesz potential, and then, the distance function Abel wavelets are derived via the fractional integral and Laplacian. Second, the DFW Weyl transform is found to be a shifted Laplace potential DFW. The DFW Radon transform is also presented. Third, we present a conjecture on truncation error formula of the multiple reciprocity Laplace DFW series and discuss its error distributions in terms of node density distributions. Forth, we point out that the Hermite distance function interpolation can be used to replace overlapping in the domain decomposition in order to produce sparse matrix. Fifth, the shape parameter is explained as a virtual extra axis contribution in terms of the MQ-type Possion kernel. The report is concluded with some remarks on a range of other issues.
Subjects: Numerical Analysis (math.NA); Computational Engineering, Finance, and Science (cs.CE)
ACM classes: G1.8, G1.2
Cite as: arXiv:cs/0207062 [cs.NA]
  (or arXiv:cs/0207062v1 [cs.NA] for this version)
  https://doi.org/10.48550/arXiv.cs/0207062

Submission history

From: Wen Chen [view email]
[v1] Mon, 15 Jul 2002 19:58:27 UTC (251 KB)
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