Regression calculation by means the minimum of maximum deflection

Very often the mean square method was used for functional approximation with the measure discrete points results. The approximation mistakes valuated by rest dispersion σ2. The regular minimax method proposed for the mistake specification The approximation results represented by the necessary dependence and two similar functions, which distinguish from its by the minimal value. There are no measured results out of the stripe. The calculation method is iterative process. Its feature was illustrated by the linear time function approximating of the dollar and euro courses fixed for the first half 2011 year. The case fixed data for a small number points discussed by course approximation during 18 weeks. The data for five days of week was known. The result was destined by the one iteration. The initial point choose by mean square method. The minimal approximation mistake contained by the intervals (1,1-1,5)σ. The two power polynomial approximation was studied with dates, fixed for the each of months. The results was after ones or two iterations. The minimum approximation mistake was after ones or two iterations. The minimum approximation mistake are (1,4-2)σ.