INTERPOLATION OF THE NAVIGATIONAL FUNCTION BY THE LAGRANGE TYPE SPLINE

The issue of any navigational isoline interpolation by cubic spline of Lagrange type has been considered in detail. The developed approach is of independent practical interest; meanwhile the task of present study is implemented in an integrated way with the finite basic method. In fact, two conceptions are majorized: a method focused on associated Lagrange multipliers in the vicinity of the optimum of the task solution and coordinate B-spline that provides iterative finding of the result within the given accuracy limits. It is demonstrated the synchronous coincidence of Lagrange splines with B-splines at nodal points using the isogeometric construction principle with difference in contours of «step-functions» and «hat-functions». The harmonized mathematical model has allowed you to realize the compromise between the Lagrange analogies and the basic finite construction for the smooth interpolation of navigational function at chaotic state of metering data «noised» by errors. The interpolation of abstract navigational isoline by set of Lagrange splines is geometrically interpreted. The detailed algorithm with new mathematical tools is presented. The task functionality can be modified before restoring the navigational isosurface on the improvised net patch. As a discussion, the author’s idea of the local interpolation applicability, provided that an additional compositional identity is introduced in order to calculate spline coefficients using explicit formulas, has been offered. The traditional formalization is transformed for logical connection establishment of spline coefficients with the measured navigational parameters. The locality allows you to manipulate invariant transformations between two different spline presentations with the formation of a single multilink attribute of bit algorithmization. Emphasis is placed on the computational advantages of the new approach on the solution stability and convergence. The hybrid unified algorithm displaces the spectrum of possibilities for processing navigational information to the search for solutions to the impossible tasks of modern navigation.

«шапочная функция», «шаговая функция», «зашумленные» данные, lagrange type spline, coordinate B-spline, «step-functions», «hat-functions», harmonized model, «noised» date, net patch, hybrid algorithm

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