Abstract: An algorithm of approximation for discrete initial numerical flow f by the first order splines, associated with the adaptive grid, is proposed. Quantitative evaluations for volumes of using data are obtained under different characteristics of regularity of initial flow. Limit characteristics of mentioned volumes are represented. Difference representations for deviation of data flow from approximate flow are done. There are discussions for pseudo-equidistant grid, grid of adaptive type and comparison of their effectiveness under condition of the same approximation. The conditions, in which the algorithm is more affective than the analogous algorithm with equidistant grid, are done.
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