Grid function approximation by linear splines with minimum deviation

Abstract

The actual application for the problem of best approximation of grid function by linear splines was formulated. A mathematical model and method of its solution were developed. Complexity of the problem was that it was multi-extremal and can not be solved analytically. This fact assumed the need to develop an efficient algorithm for solving the problem.The method was developed for solving the problem of dynamic programming scheme, which was extended by us. In some studies, a similar problem was solved locally, and their solution did not include a large number of segments. However, in this paper, the problem was solved globally with defect delta.Given the application of the method to the problem of flow control in the pressure regulating systems, the pipeline network for transport of substances (pipelines of oil, gas, water, etc.) minimises the amount of substance in reservoirs and reduces the discharge of substance from the system. The method and algorithm developed may be used in computational mathematics, optimum control and regulation system, and regressive analysis.