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For the first time, the formalization of the least squares method is presented as matrix calculation with the purpose of optimal approximation of the navigational isosurface as the geometric image of navigational isolines concentration in the context of modern understanding of the navigational field concept. The task topicality is specified by the necessity to search a new decision for parallelization of blocky matrix transformations organizing in the navigation practice due to the measurements superfluity as the result of doubling the ship’s position definition by the alternative methods. The pragmatic estimation of the classic mathematical apparatus doesn’t exclude the possibility of the negative problem manifestation of looping a computer program realizing the standard least squares method. In the existing mathematical approach there is no algorithmic ability of adaptation to the potential resource of the multiprocessor computer equipment. The computational stability of new method is determined by the ability to repeatedly use the computational module in the algorithm to solve an ultra-large system of linear algebraic equations using symmetric techniques with cellular matrices. The visual geometrical interpretation of the hybrid interpolation technology of a hypothetical fragment of the navigational isosurface in 3D projection is presented. The intuitive selection of the controlled smoothing parameter in an interactive mode for choosing between interpolation and approximation depending on the navigational measurements accuracy is realized. The study of searching an optimization scheme for organizing grid nodes acquires an independent mathematical interest. The issue of high-speed information handling on the base of modified formula at its realization in the onboard computer to ensure the navigator’s adequate analysis the incoming data flow, the proper variation of the watch staff and avoiding the crew fatigue, as well as assistance in the correct decision making regarding ship management, is examined. When applying the formula derived in the proposed study, a double effect is achieved simultaneously: improving the final results accuracy and organizing the effective calculations by optimizing the computational costs.

vestnik gosudarstvennogo universiteta morskogo i rečnogo flota imeni admirala s. o. makarova/vestnik gosudarstvennogo universiteta morskogo i rečnogo flota imeni admirala s.o. makarova

MODIFICATION OF THE LEAST SQUARES METHOD FOR SPLINE APPROXIMATION OF NAVIGATIONAL ISOSURFACE