Convergence analysis of Sakurai–Torii–Sugiura iterative method for simultaneous approximation of polynomial zeros

Local and Semilocal Convergence of Wang-Zheng’s Method for Simultaneous Finding Polynomial Zeros

“…Our local convergence result of the second type is the first result of this type for Wang-Zheng's method (1). The convergence results of the second type for other simultaneous methods can be found in [17,[22][23][24]28,29].…”

“…Finally, we refer the reader to some recent papers [2,17,20,[22][23][24][25]28,29], which investigate initial conditions of the type (66).…”

“…On the basis of this theory lays the notion function of initial conditions of T since the convergence of any iterative method of the type (1) is studied with respect to some function of initial conditions (see [35,36]). Some applications of this theory can be found in [1,2,5,7,8,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][35][36][37][38]. Let R n be equipped with coordinate-wise ordering defined by:…”

“…where the function W f : D ⊂ K n → K n is defined by (7). Henceforth, we use a metric ρ on K n , which was introduced in [23]. First, we define an equivalence relation ≡ on K n as follows: x ≡ y if there exists a permutation (i 1 , .…”

Inverse Numerical Iterative Technique for Finding all Roots of Nonlinear Equations with Engineering Applications

“…ere is another class of derivative-free iterative methods which approximates all roots of (1) simultaneously. e simultaneous iterative methods for approximating all roots of (1) are very popular due to their global convergence and parallel implementation on computer (see, e.g., Weierstrass [3], Kanno [4], Proinov [5], Petkovi´c [6], Mir [7], Nourein [8], Aberth [9], and reference cited there in [10][11][12][13][14][15][16][17][18][19][20][21][22]).…”