# Investigation of solutions of the nonlinear synthesis problem for linear array by the generalized Newton method

## DOI:

https://doi.org/10.1109/ICATT.2009.4435135## Keywords:

amplitude radiation pattern, variational statement, non-linear integral equation, generalized Newton method## Abstract

The synthesis problem for linear array according to the prescribed amplitude radiation pattern is considered in the variational statement. The functional representing the weighted inner product of prescribed and synthesized amplitude radiation patterns is used. The problem reduces to solving the non-linear integral equation. The generalized Newton procedure is used for search of solutions. The results of numerical calculations are given for several types of prescribed amplitude radiation pattern.## References

ANDRIYCHUK, M.I.; VOITOVICH, N.N.; SAVENKO,P.A.; TKACHUK, V.P. *The Antenna Synthesis According to the Amplitude Radiation Pattern. Numerical Methods and Algorithms.* Kiev: Naukova Dumka, 1993 [in Russian].

DEUFLHARD, P. *Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms*. Series Computational Mathematics, v.35. Springer, 2004.

BULATSYK, O.O.; KATSENELENBAUM, B.Z.; TOPOLYUK, Y.P.; VOITOVICH, N.N. *Phase Optimization Problems. Application in Wave Field Theory.* Berlin: Wiley-VCH.

BULATSYK, O.O.; VOITOVICH, M.N. Analytical Solutions to a Class of Non-linear Integral Equations Connected with Modified Phase Problem. *Information Extracting and Processing*, 2003, v.19, p.33-39.

## Published

2009-10-10

## Issue

## Section

Antenna arrays