Spline іnterfletation method in finding the largest (least) values for function of three variables in multiextreme tasks
Keywords:
operators of spline-interlineation, operators of spline-іnterfletation, tracks of function, system mutually perpendicular linesAbstract
The decision of many practical tasks in the sphere of economy, management, technique and engineer puts new and new tasks for the theory of optimization. An aim of optimization is finding the largest or the least value among potentially possible. This aim can be achieved by various methods. Among them - the methods of discrete, undifferentiated and stochastic optimization. Interpolation methods are more widely used now in the mathematical modeling of many industries and spheres of activity. Unfortunately, authors often use only individual points values of the investigated function in the construction of appropriate algorithms of optimization methods.
In this article for the solution of task of finding the largest and the least values of continuous function of three variables in the closed domain it is offered to use operators of spline interlineation on the system mutually perpendicular lines, built by means of operators of spline interflatation function of three variables. It is used method of reduction of general task to the sequence of tasks of finding the approximate largest or least value of function on the system mutually perpendicular lines. In this work theorems and their proofs are described. Theorems are about the spline- іnterfletation operator and its properties, spline-interlineation operator and its properties and error in the approximation of a function by spline-interlineation operator. An example of finding the least value of function of three variables is examined. Solution steps are described. Calculated data testify to efficiency of the offered and investigated method of using spline-interlineation operators on the system mutually perpendicular lines built by means of spline-interflatation operators of three variables function. Authors intend to use the offered method to find the largest (the least) value of function of n variables.References
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