A Novel Family of Efficient Weighted-Newton Multiple Root Iterations

Symmetry

Deepak Kumar¹  Janak Raj Sharma²  Lorentz Jăntschi³ 

[1] Department of Mathematics, Chandigarh University, Mohali 104413, India;Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal 148106, India;Department of Physics and Chemistry, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania;

关键词: nonlinear equations;    multiple roots;    Newton method;    fast algorithms;    efficiency;   

DOI  :  10.3390/sym12091494

来源: DOAJ

【 摘 要 】

We propose a novel family of seventh-order iterative methods for computing multiple zeros of a nonlinear function. The algorithm consists of three steps, of which the first two are the steps of recently developed Liu–Zhou fourth-order method, whereas the third step is based on a Newton-like step. The efficiency index of the proposed scheme is 1.627, which is better than the efficiency index 1.587 of the basic Liu–Zhou fourth-order method. In this sense, the proposed iteration is the modification over the Liu–Zhou iteration. Theoretical results are fully studied including the main theorem of local convergence analysis. Moreover, convergence domains are also assessed using the graphical tool, namely, basins of attraction which are symmetrical through the fractal like boundaries. Accuracy and computational efficiency are demonstrated by implementing the algorithms on different numerical problems. Comparison of numerical experiments shows that the new methods have an edge over the existing methods.

【 授权许可】

Unknown