Abstract
A regularization method is proposed for the function reconstruction from approximate average fluxes. Such problems often occur in environmental science and mathematical statistics. The unique solvability of the method is proved and a number of conditions are given to characterize the solution. The error estimates are established after the introduction of some interpolation operators. A series of numerical examples are provided to illustrate the effectiveness and computational performance of the method. Some ideas for the choice of the regularization parameter are also suggested by the computational experience.
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