On the stability of meshless symmetric collocation for boundary value problems

Wendland, Holger (2007) On the stability of meshless symmetric collocation for boundary value problems. BIT Numerical Mathematics, 47 (2). pp. 455-468. ISSN 0006-3835

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Abstract

In 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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Holger Wendland
Date Deposited: 06 Feb 2012 19:34
Last Modified: 09 Jul 2012 14:32
URI: http://sro.sussex.ac.uk/id/eprint/21338
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