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The study of nonlinear matrix equations, in particular, the algebraic matrix Riccati equation [1,2,3], is connected with numerous applications of such equations in solving the differential matrix Riccati equation [2,3], in the theory of nonlinear oscillations, in mechanics, biology, and radiotechnology, the theory of control and stability of motion, and others. We used the Newton-Kantorovich method [3] and the Adomian decomposition method to find approximations for the solutions of nonlinear matrix equations in the case of an unknown rectangular matrix [4,5].
This work was partially supported by a grant from the Simons Foundation (PD-Ukraine-00010584, K.S. Shevtsova).
[1] Samoilenko A.M., Boichuk A.A., Krivosheya S.A. Boundary value problems for systems of integro-differential equations with Degenerate Kernel. Ukrainian Mathematical Journal. 1996, 48(11}, P. 1785-1789.
[2] Boichuk A.A., Krivosheya S.A. A Critical periodic boundary value problem for a matrix Riccati equation. Differential Equations. 2001, 37(4), P. 464-471.
[3] Chuiko S.M., Shevtsova K.S. Solvability conditions for nonlinear matrix equations. Journal of Mathematical Sciences. 2023, 270(3), P. 407-419.
[4] Adomian G. A review of the decomposition method in applied mathematics. Journ. of Math. Math. Anal. and Appl. 1988, 135, P. 501-544.
[5] Chuiko S.M., Chuiko O.S., Popov M.V. Adomian decomposition method in the theory of nonlinear boundary-value problems. Journal of Mathematical Sciences. 2023, 277(2), P. 338-351.
