Using matrix eigenvalues to construct an iterative method with the highest possible efficiency index two
Document Type
Article
Publication Date
5-1-2022
Abstract
In this paper, we first derive a family of iterative schemes with fourth order. A weight function is used to maintain its optimality. Then, we transform it into methods with several self-accelerating parameters to reach the highest possible convergence rate 8. For this aim, we employ the property of the eigenvalues of the matrices and the technique with memory. Solving several nonlinear test equations shows that the proposed variants have a computational efficiency index of two (maximum amount possible) in practice.
Keywords
With-memory method, Accelerator parameter, R-order convergence, Eigenvalues
Divisions
Science
Funders
Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia (Grant No: KEP-48-130-42
Publication Title
Mathematics
Volume
10
Issue
9
Publisher
MDPI
Publisher Location
ST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND