6533b858fe1ef96bd12b6b78

RESEARCH PRODUCT

�ber ein Verfahren der Ordnung $$1 + \sqrt 2 $$ zur Nullstellenbestimmung

Wilhelm Werner

subject

Iterative methodApplied MathematicsNumerical analysisFunction (mathematics)Computational Mathematicssymbols.namesakeNonlinear systemConvergence (routing)symbolsCalculusApplied mathematicsDifferentiable functionNewton's methodMathematics

description

A new iterative method for solving nonlinear equations is presented which is shown to converge locally withR-order of convergence $$1 + \sqrt 2 $$ at least under suitable differentiability assumptions. The method needs as many function evaluations per step as the classical Newton method.

https://doi.org/10.1007/bf01397005