A Digital-Discrete Method For Smooth-Continuous Data Reconstruction
For researchers needing smooth function reconstruction from discrete data, this method provides an alternative to existing techniques, though it is incremental.
The paper presents a digital-discrete method for reconstructing smooth continuous functions from sample data, validated on real groundwater data. The method offers advantages over existing approaches like cubic splines and finite elements.
A systematic digital-discrete method for obtaining continuous functions with smoothness to a certain order (C^(n)) from sample data is designed. This method is based on gradually varied functions and the classical finite difference method. This new method has been applied to real groundwater data and the results have validated the method. This method is independent from existing popular methods such as the cubic spline method and the finite element method. The new digital-discrete method has considerable advantages for a large number of real data applications. This digital method also differs from other classical discrete methods that usually use triangulations. This method can potentially be used to obtain smooth functions such as polynomials through its derivatives f^(k) and the solution for partial differential equations such as harmonic and other important equations.