Abstract
AbstractThis paper considers the regularization theory based on the general regression. The general regression does not require the measure for the smoothness, which plays the important role in the standard regularization theory or its extension. The theory is extended so that the regularization can be applied to the case where the data are multivalued. Based on the extended theory, an algorithm is derived which can reconstruct in a deterministic way the discontinuous function from the discrete data, without requiring the conventional line process, by regarding the discontinuity as a boundary between different functions. The effectiveness of the derived algorithm and the robustness against the noise are demonstrated by a computer simulation.
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