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In this paper we consider the ill-posed problem of recovery of a function which has a finite number of jumps using noised data. The method which we suggest allows us to find a number of discontinuities. The position of the discontinuity points and the values of jumps are derived approximately. The estimates of accuracy of positions and jumps values are given. Approximation of initial function is constructed. The uniform estimate of proximity of the approximate function and the exact function is given outside the neighborhoods discontinuity points.

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