Extending the convergence domain of the Secant and Moser method in Banach Space

Abstract

MSC: 65J15 47H17 Keywords: Newton's method Secant method Moser method Semilocal convergence Recurrent relations Banach space a b s t r a c t We present a new semilocal convergence analysis for the Secant and the Moser method in order to approximate a solution of an equation in a Banach space setting. Using the method of recurrent relations and weaker sufficient convergence criteria than in earlier studies such as Amat et al. (2014), Hernández and Rubio (2007), Hernández and Rubio (1999) and Hernández and Rubio (2002) we increase the convergence domain of these methods. The advantages are also obtained under less computational cost than in Amat et al. (2014), Hernández and Rubio (2007), Hernández and Rubio (1999) and Hernández and Rubio (2002). Numerical examples where the older convergence criteria are not satisfied but the new convergence criteria are satisfied are also provided in this study.

A Class of Novel Mann-Type Subgradient Extragradient Algorithms for Solving Quasimonotone Variational Inequalities

“…It is well-established that the problem ( 1) is a key problem in nonlinear analysis. It is an important mathematical model that incorporates many important topics in pure and applied mathematics, such as a nonlinear system of equations, optimization conditions for problems with the optimization process, complementarity problems, network equilibrium problems and finance (see [3][4][5][6][7][8][9][10][11][12][13] and others in [14][15][16][17][18][19]). As a result, this problem has a number of applications in engineering, mathematical programming, network economics, transportation analysis, game theory and software engineering.…”