Convergence of discrete and penalized least squares spherical splines |
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Authors: | Victoria Baramidze Ming-Jun Lai |
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Affiliation: | 1. Department of Mathematics, Western Illinois University, 1 University Circle, Macomb, IL 61455, USA;2. Department of Mathematics, The University of Georgia, Athens, GA 30602, USA |
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Abstract: | We study the convergence of discrete and penalized least squares spherical splines in spaces with stable local bases. We derive a bound for error in the approximation of a sufficiently smooth function by the discrete and penalized least squares splines. The error bound for the discrete least squares splines is explicitly dependent on the mesh size of the underlying triangulation. The error bound for the penalized least squares splines additionally depends on the penalty parameter. |
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