Iterative schemes for finding all roots simultaneously of nonlinear equations
Alicia Cordero, Neus Garrido, Juan R. Torregrosa, Paula Triguero‐Navarro
Abstract
In this paper, we propose a procedure that can be added to any iterative scheme in order to turn it into an iterative method for approximating all roots simultaneously of any nonlinear equations. By applying this procedure to any iterative method of order p, we obtain a new scheme of order of convergence 2p. Some numerical tests allow us to confirm the theoretical results and to compare the proposed schemes with other known methods for simultaneous roots of polynomial and non-polynomial functions.
Topics & Concepts
MathematicsConvergence (economics)PolynomialNonlinear systemIterative methodLocal convergenceScheme (mathematics)Applied mathematicsOrder (exchange)Mathematical optimizationMathematical analysisFinanceQuantum mechanicsPhysicsEconomicsEconomic growthIterative Methods for Nonlinear EquationsAdvanced Optimization Algorithms ResearchAdvanced Numerical Analysis Techniques