Using matrix eigenvalues to construct an iterative method with the highest possible efficiency index two

Authors

• Malik Zaka Ullah
• Vali Torkashvand
• Stanford Shateyi
• Mir Asma

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

Publication Title

Mathematics

Recommended Citation

Ullah, Malik Zaka; Torkashvand, Vali; Shateyi, Stanford; and Asma, Mir, "Using matrix eigenvalues to construct an iterative method with the highest possible efficiency index two" (2022). Research Publications (2021 to 2025). 214.
https://knova.um.edu.my/research_publications_2021_2025/214

Divisions

Science

Funders

Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia (Grant No: KEP-48-130-42

Volume

10

Issue

9

Publisher

MDPI

Publisher Location

ST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND