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ON REALIZATION OF LIMIT POLYGONS IN SEQUENTIAL PROJECTION METHOD |
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| รหัสดีโอไอ | |
| Creator | N. M. Mishachev, Anatoly Mikhailovich Shmyrin |
| Title | ON REALIZATION OF LIMIT POLYGONS IN SEQUENTIAL PROJECTION METHOD |
| Contributor | - |
| Publisher | TuEngr Group |
| Publication Year | 2562 |
| Journal Title | International Transaction Journal of Engineering, Management, & Applied Sciences & Technologies |
| Journal Vol. | 10 |
| Journal No. | 15 |
| Page no. | 10A15G: 1-5 |
| Keyword | Kaczmarz algorithm, Limit polygon, Sequential projections, Affine operator, Sequence of hyperplanes, Overdetermined linear systems. |
| URL Website | http://tuengr.com/Vol10_15.html |
| Website title | ITJEMAST V10(15) 2019 @ TuEngr.com |
| ISSN | 2228-9860 |
| Abstract | In this article, we study the properties of the algorithm for solving systems of linear equations based on the sequential projections of an initial approximation point on the hyperplanes, defined by the equations of the system (Kaczmarz algorithm). We consider the case of overdetermined systems when the sequence of approximations converges to a limit cycle, the points of which we regard as the vertices of a limit polygon. Although the proof of convergence to the limit polygon is known, we are discussing a simplified version, relating to the case of general position and clarifying the main idea of the proof. The properties of the limit polygon are little studied, but at the same time, they are important for applications. We explain that, with a proper choice of a system of equations, the limit polygon can be any predefined polygon. In other words, there are no restrictions on the type of limit polygon. |
