Applications of the Digital-Discrete Method in Smooth-Continuous Data Reconstruction. (arXiv:1002.2367v2 [math.NA])

Applications of the Digital-Discrete Method in Smooth-Continuous Data Reconstruction. (arXiv:1002.2367v2 [math.NA]): "

This paper presents some applications of using recently developed algorithms
for smooth-continuous data reconstruction based on the digital-discrete method.
The classical discrete method for data reconstruction is based on domain
decomposition according to guiding (or sample) points. Then uses Splines (for
polynomial) or finite elements method (for PDE) to fit the data. Our method is
based on the gradually varied function that does not assume the property of the
linearly separable among guiding points, i.e. no domain decomposition methods
are needed. We also demonstrate the flexibility of the new method and the
potential to solve variety of problems. The examples include some real data
from water well logs and harmonic functions on closed 2D manifolds. This paper
presented the results from six different algorithms. This method can be easily
extended to higher multi-dimensions.

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