The non-iterative algorithm that reveals the general physical basis of measuring processes and instrumental (computer) computations is proposed and investigated. The algorithm is based on the previously proposed postulate and consists in finding the optimal, locally defined width of the averaging interval. The optimal width of the interval provides the smallest error when measuring or computing the changing magnitude. The technology of the algorithm consists in adaption of parameters of a measuring device to parameters of the measured object at every measurement or computation step. The efficiency of the algorithm has been successfully tested with a number of standard numerical solutions.