Applications of the Digital-Discrete Method in Smooth-Continuous Data Reconstruction

Abstract

This paper presents some applications 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 the Spline method (for polynomial) or finite elements method (for PDE) is used to fit the data. Our method is based on the gradually varied function that does not assume the property of being linearly separable among guiding points, i.e. no domain decomposition methods are needed. We also demonstrate the flexibility of the new method and its potential to solve a variety of problems. The examples include some real data from water well logs and harmonic functions on closed 2D manifolds. This paper presents the results from six different algorithms. This method can be easily extended to higher multi-dimensions. We also include an advanced consideration related to the use of gradually varied mapping.