Local convergence of Newton-HSS methods with positive definite Jacobian matrices under generalized conditions
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We study the local convergence of Newton-HSS method and modified Newton-HSS method to approximate a locally unique solution of a nonlinear equation under generalized conditions. Our conditions when specialized to Lipschitz conditions considered in earlier studies provide tighter error estimates on the distances involved and a larger radius of convergence leading to fewer iterates to achieve a desired error tolerance and a wider choice of initial guesses. Hence, the applicability of the methods is expanded. Finally, numerical tests are also performed to show that our results apply to solve equations in cases where earlier study cannot apply.
KeywordsNewton-HSS method Local convergence System of nonlinear equations Generalized Lipschitz conditions
Mathematics Subject Classification65F10 65W05
- 7.Argyros, I.K., Sharma, J.R., Kumar, D.: Ball convergence of the Newton–Gauss method in Banach space. SeMa (2016). doi: 10.1007/s40324-016-0091-z