List of publications on a keyword: «интерполяция»

The paper deals with iterative interpolation methods in forms of similar recursive procedures defined by a sort of simple functions (interpolation basis) not necessarily real valued. These basic functions are kind of arbitrary type being defined just by wish and considerations of user. The studied interpolant construction shows virtue of versatility: it may be used in a wide range of vector spaces endowed with scalar product, no dimension restrictions, both in Euclidean and Hilbert spaces. The choice of basic interpolation functions is as wide as possible since it is subdued nonessential restrictions. The interpolation method considered in particular coincides with traditional polynomial interpolation (mimic of Lagrange method in real unidimensional case) or rational, exponential etc. in other cases. The interpolation as iterative process, in fact, is fairly flexible and allows one procedure to change the type of interpolation, depending on the node number in a given set. Linear interpolation basis options (perhaps some nonlinear ones) allow to interpolate in noncommutative spaces, such as spaces of nondegenerate matrices, interpolated data can also be relevant elements of vector spaces over arbitrary numeric field. By way of illustration, the author gives the examples of interpolation on the real plane, in the separable Hilbert space and the space of square matrices with vektorvalued source data.

It was noted in the article, that initially the problem of interpolation of the simple plane curve arose in the problem of simulation of subsonic flow around a body with the subsequent calculation of the velocity potential using the vortex panel method. However, as it turned out, the practical importance of this method is much wider. This algorithm can be successfully applied in any task that requires a discrete set of points which describe an arbitrary curve: potential function method, flow around an airfoil with the trailing edge (airfoil, liquid drop, etc.), analytic expression, which is very difficult to obtain, creation of the font and logo and in some tasks of architecture and garment industry.

The article discusses the construction of splines interpolation of varying degree and compares their features, the spline is described in this article as a function, which is divided into the final number of pieces and the spline coincide with some polynomial on each of these pieces.

В данной статье авторами рассматривается понятие «интерполяция» с точки зрения математики, а также объясняется ее применение в сфере обработки изображений.

В данной статье рассматривается понятие интерполяционного полинома произвольной степени и способы его построения.

При кинематическом анализе кулачковых механизмов, профили которых заданы таблично или получены в результате замеров методом малых делений, возникают системные искажения кинематических характеристик, которые в свою очередь вызывают осцилляции на графиках скоростей и ускорений. В этом случае для определения аналитического закона движения ведомого звена необходимо проводить «сглаживание» полученных значений