Error Bounds for Solving Pseudodifferential Equations on Spheres by Collocation with Zonal Kernels |
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| Authors: | Tanya M Morton Marian Neamtu |
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| Institution: | Center for Constructive Approximation, Department of Mathematics, Vanderbilt University, Nashville, Tennessee, 37240, U.S.A.f1 |
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| Abstract: | The problem of solving pseudodifferential equations on spheres by collocation with zonal kernels is considered and bounds for the approximation error are established. The bounds are given in terms of the maximum separation distance of the collocation points, the order of the pseudodifferential operator, and the smoothness of the employed zonal kernel. A by-product of the results is an improvement on the previously known convergence order estimates for Lagrange interpolation. |
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| Keywords: | pseudodifferential equation collocation zonal kernel interpolation approximation order sphere positive definite function radial basis function |
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