Error indicators and adaptive refinement of the discrete thin plate spline smoother

Abstract

The discrete thin plate spline is a data fitting and smoothing technique for large datasets. Current research only uses uniform grids for this discrete smoother, which may require a fine grid to achieve a certain accuracy. This leads to a large system of equations and high computational costs. Adaptive refinement adapts the precision of the solution to reduce computational costs by refining only in sensitive regions. The error indicator is an essential part of the adaptive refinement as it identifies whether certain regions should be refined. Error indicators are well researched in the finite element method, but they might not work for the discrete smoother as data may be perturbed by noise and not uniformly distributed. Two error indicators are presented: one computes errors by solving an auxiliary problem and the other uses the bounds of the finite element error. Their performances are evaluated and compared with 2D model problems. References

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