Physics, mathematics, and technology

2020 Issue №3

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On the problem of evaluating the accuracy of di-agnostics of wave disturbances carried out using the technique of projec­tion operators



In this note we study the problem of a function reconstruction in a con­text of a Laplace method application. We use a unitary space of splines with a double dimension of one, that approximate the set of points, representing the results of observation. The conventional scalar product allows to project the approximation onto the subspace of observations. The use of the same scalar product yields the norm that we use to estimate error deviations within the model under consideration. Its minimum defines both a function reconstruc­tion and its error, which also include the measurements errors. The results we apply to the problems of reconstruction of initial or boundary conditions for 1D wave equation, that imply the procedure of directed waves division.