The Investigation on Two Kinds of Nonlinear Matrix Equations

Positive coincidence points for a class of nonlinear operators and their applications to matrix equations

“…where Q is a positive semi definite matrix, A i are arbitrary square matrices, f i are Löwner-Heinz monotone operators and g is an Uchiyama operator [16][17][18]. Our results improve, extend and generalize some existing ones in the literature [11,15,19,20]. Furthermore, we provide two algorithms involving the Newton-Raphson method for solving new classes of nonlinear matrix equations.…”

“…The coincidence point theory is a powerful tool in nonlinear analysis for solving a wide range of nonlinear equations arising from various applications in engineering, economics and mechanics, see for instance [1][2][3][4][5][6][7][8]. In particular, nonlinear equations in Banach spaces involving α-concave and α (− )-convex operators are considered in [9][10][11][12][13][14][15] and some references therein.…”

The Feasibility of Homotopy Continuation Method for a Nonlinear Matrix Equation

“…Some special cases of matrix equation 1and related matrix equations were studied on the solvability, numerical methods, and perturbation analysis by many scholars: [24]; and X s ± A * F(X)A � Q [25][26][27][28][29]. In addition, many homotopy approaches oriented toward engineering applications were investigated by many scholars: the homotopy analysis method (HAM) [30], the Optimal Homotopy Asymptotic Method (OHAM) [31], the Optimal Homotopy Perturbation Method (OHPM) [32], the homotopy asymptotic method [33], and so on.…”