A family of Newton-type methods with seventh and eighth-order of convergence for solving systems of nonlinear equations
Т. Жанлав, R. Mijiddorj, Khuder Otgondorj
Abstract
In this work, we first develop a new family of three-step seventh- and eighth-order Newton-type iterative methods for solving systems of nonlinear equations. We also propose some different choices of parameter matrices that ensure the convergence order. The proposed family includes some known methods as special cases. The computational cost and efficiency index of our methods are discussed. Numerical experiments are conducted to support the theoretical results.
Topics & Concepts
MathematicsConvergence (economics)Nonlinear systemNewton's methodLocal convergenceType (biology)Applied mathematicsOrder (exchange)Iterative methodWork (physics)Mathematical optimizationEngineeringEconomicsEcologyFinancePhysicsEconomic growthQuantum mechanicsBiologyMechanical engineeringIterative Methods for Nonlinear EquationsAdvanced Optimization Algorithms ResearchMatrix Theory and Algorithms