On the convergence of Gander’s type family of iterative methods 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:…”

Computer Methodologies for the Comparison of Some Efficient Derivative Free Simultaneous Iterative Methods for Finding Roots of Non-Linear Equations

“…On the other hand, there are lot of numerical iterative methods devoted to approximate all roots of Eq. ( 1) simultaneously (see, e.g., [1,[5][6][7][8] and the references therein). The SIM are popular as compared to single root finding methods due to their wider range of convergence, reliability and their applications for parallel computing as well.…”

“…The SIM are popular as compared to single root finding methods due to their wider range of convergence, reliability and their applications for parallel computing as well. Further details on SIM, their convergence analysis, efficiency and parallel implementations can be seen in [9,[10][11][12][13] and references cited there in. The main objective of this article is to construct SIM which have more efficient and higher convergence order for approximating all distinct roots of Eq.…”