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On the stability of meshless symmetric collocation for boundary value problems
journal contribution
posted on 2023-06-07, 23:25 authored by Holger WendlandIn this paper, we study the stability of symmetric collocation methods for boundary value problems using certain positive definite kernels. We derive lower bounds on the smallest eigenvalue of the associated collocation matrix in terms of the separation distance. Comparing these bounds to the well-known error estimates shows that another trade-off appears, which is significantly worse than the one known from classical interpolation. Finally, we show how this new trade-off can be overcome as well as how the collocation matrix can be stabilized by smoothing.
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Publication status
- Published
Journal
BIT Numerical MathematicsISSN
0006-3835Publisher
SpringerExternal DOI
Issue
2Volume
47Page range
455-468Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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