QUASI-ANALYTICAL METHOD FOR IMAGES CONSTRUCTION FROM GRAVITATIONAL LENSES

A. T. Kotvytskiy, S. D. Bronza

Анотація


One of the main problems in the study of system of equations of the gravitational lens, is the computation of coordinates from the known position of the source. In the process of computing finds the solution of equations with two unknowns. The problem is that, in general, there is no analytical method that can find all of the roots (lens) of system over the field of real numbers. In this connection, use numerical methods like the method of tracing. For the N-point gravitational lenses we have a system of polynomial equations. The methods of algebraic geometry, we transform the system to another system, which splits into two equations. Each equation of the transformed system is a polynomial in one variable. Finding the roots of these equations is the standard computing task.


Ключові слова


Lens: gravitational lenses; binary lenses; Algebraic geometry: resultant

Повний текст:

PDF (English)

Посилання


Blioch P.V., Minakov A.A.: 1989, Gravitacionnye linzy, 240 p.

Weinberg S.: 1972, Gravitation and Cosmology, 696.

Landau L.D., Lifshitz E.M.: 1988, The classical Theory of Fields, V.2, 512 p.

Zakharov A.F.: 1997, Gravitacionnye linzy i mikro- linzy, 328 p.

Schneider P., Ehlers J., Falco E.E.: 1999, Gravitational lenses, 560 p.

Chwolson O.: 1924, Astr. Nachrichten., 221, 329.

Einstein A.: 1936 Science., 2188, 506.

Schneider P., Weiss A.: 1986, Astr. Ap., 164, 237.

Asada H.: 2002, Astron. Astrophys., 390, L11.

Cassan A.: 2008, Astron. Astrophys., 491, 587.

Witt H.J.: 1990, Astron. Astrophys., 236, 311.

Lang S.: 1965, Algebra, 564 p.

Walker R.J.: 1950, Algebraic curves, 236 p.

Van Der Waerden B.L.: 1971, Algebra I, II, 456 p.




DOI: http://dx.doi.org/10.18524/1810-4215.2016.29.84958

Посилання

  • Поки немає зовнішніх посилань.


Copyright (c) 2016 Odessa Astronomical Publications

Creative Commons License
Ця робота ліцензована Creative Commons Attribution-NonCommercial 4.0 International License.