Polynomial interpolation with known projections on an arbitrary system of N groups of lines consisting of M parallel lines
Given N groups of lines, each consisting of M parallel lines. Each line of the group overlaps with all other lines from (N–1) group. It is believed that in the points of intersection of these lines there are given finite function values f(x, y) continuous together with its derivatives of the first o...
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| Date: | 2014 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Інститут енергетичних машин і систем ім. А. М. Підгорного Національної академії наук України
2014
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| Subjects: | |
| Online Access: | https://journals.uran.ua/jme/article/view/31411 |
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| Journal Title: | Energy Technologies & Resource Saving |
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Energy Technologies & Resource Saving| Summary: | Given N groups of lines, each consisting of M parallel lines. Each line of the group overlaps with all other lines from (N–1) group. It is believed that in the points of intersection of these lines there are given finite function values f(x, y) continuous together with its derivatives of the first order, the carrier of which is a square [0, 1]´[0, 1]. The projections are considered to be known, where the integrals along each of the n´m line, coming from CT. In fact, these integrals are along line segments that cross media. This paper solves the following problem: to build an operator approximation function f(x, y), which not only interpolates the function in these nodes, but also has given projections. The results of this study can be used in non-destructive testing of important parts in mechanical engineering. |
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