Universal methods for solving model equations for the dimensional calculation of optical systems

Иванов А.В. Универсальные методы решения модельных уравнений при габаритном расчете оптических систем // Оптический журнал. 2007. Т. 74. № 5. С. 7–11.

Ivanov A.V. Universal methods for solving model equations for the dimensional calculation of optical systems [in Russian] // Opticheskii Zhurnal. 2007. V. 74. № 5. P. 7–11.

A. V. Ivanov, "Universal methods for solving model equations for the dimensional calculation of optical systems," Journal of Optical Technology. 74 (5), 302-306 (2007). https://doi.org/10.1364/JOT.74.000302

This paper proposes high-efficiency universal methods for the parametric synthesis of centered optical systems in the Gaussian region, using algebraic, numerical, and mixed approaches to the solution of systems of multilinear model equations. The algebraic method is based on polynomial simplification, using the resultants of the polynomials or constructing the Gröbner basis of the ideal generated by the polynomials. The numerical algorithm is based on the necessary conditions formulated by the author for the existence of solutions. Examples of the operation of the proposed parametric-synthesis methods are given.