6533b85bfe1ef96bd12bb35d
RESEARCH PRODUCT
A class of third order iterative Kurchatov–Steffensen (derivative free) methods for solving nonlinear equations
Vicente F. CandelaRosa M. Perissubject
0209 industrial biotechnologyClass (set theory)Computer scienceIterative methodApplied MathematicsStability (learning theory)020206 networking & telecommunications02 engineering and technologyChebyshev filterComputational MathematicsNonlinear systemThird order020901 industrial engineering & automationRate of convergenceConvergence (routing)0202 electrical engineering electronic engineering information engineeringApplied mathematicsdescription
Abstract In this paper we show a strategy to devise third order iterative methods based on classic second order ones such as Steffensen’s and Kurchatov’s. These methods do not require the evaluation of derivatives, as opposed to Newton or other well known third order methods such as Halley or Chebyshev. Some theoretical results on convergence will be stated, and illustrated through examples. These methods are useful when the functions are not regular or the evaluation of their derivatives is costly. Furthermore, special features as stability, laterality (asymmetry) and other properties can be addressed by choosing adequate nodes in the design of the methods.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-06-01 | Applied Mathematics and Computation |