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BIT Numerical Mathematics

, Volume 47, Issue 2, pp 455–468 | Cite as

On the stability of meshless symmetric collocation for boundary value problems

  • Holger WendlandEmail author
Article

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.

Key words

scattered data collocation elliptic problems stability 

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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SussexBrightonEngland

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