THE TECHNIQUE FOR SPLINE APPROXIMATIONS BUILDING IN CONDITIONS OF LIMITED SOURCE DATA
Abstract
Mathematical modeling is widely applied in different fields of activity but in cases when the available numerical information is insufficient to get a complete picture of the object mathematical model building is difficult or can lead to a deliberately unreliable result. There are approaches to solving modeling problems with a lack of data therewith it may be necessary to use methods with complicated mathematical structure to get the desired result. In this regard, the task of adapting mathematical methods to data scarcity conditions is relevant. This paper discusses the solution of the interpolation problem using spline functions as one of the most widely used methods in mathematical theory and applied mechanics. A technique has been developed to adapt spline methods to data shortage conditions, applying this technique to building of a cylinder with elliptical bottoms forming model provided smooth joining of fragments and absence of kinks. Meeting the requirements of precision and smoothness of the model was achieved by sequential refinement of numerical data with adding interpolation nodes to the model and correction of their location. As a result of building and analysis of the model it was found that spline methods can be applied to solving interpolation problems of almost any complexity. The availability of an analytical justification for every step of modeling process allows to automate the process fully. The problem considered in the article is connected with manufacturing products on the numerically controlled machines. However, this technique due to its versatility can be applied to solving problems in various fields of activity. The practical value of the developed technique is the possibility of its application to many practical tasks. Its integration into modern CAD systems and application software packages will allow to expand their functionality by providing the user with the possibility to introduce the extra restrictions imposed on the model practically what can ensure a high degree of implementation flexibility.
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