Consistency method for measurements of the support function of a convex body in the metric of $L_{\infty}$

A new algorithm is proposed for estimation of convex body support function measurements in $L_{\infty}$ metric, which allows us to obtain the solution in quadratic time (with respect to the number of measurements) not using linear programming. The rate of convergence is proved to be stable for quite weak conditions on input data. This fact makes the algorithm robust for a wider class of problems than it was previously. The implemented algorithm is stable and predictable unlike other existing support function estimation algorithms. Implementation details and testing results are presented.