Extending the applicability of a third-order scheme with Lipschitz and Hölder continuous derivative in Banach spaces

Journal of the Egyptian Mathematical Society

Sanjaya Kumar Parhi¹  Debasis Sharma¹ 

[1] Department of Mathematics, International Institute of Information Technology Bhubaneswar;

关键词: Local convergence;    Iterative schemes;    Banach space;    Lipschitz continuity condition;    Hölder continuity condition;   

DOI  :  10.1186/s42787-020-00088-2

来源: DOAJ

【 摘 要 】

Abstract We extend the applicability of a cubically convergent nonlinear system solver using Lipschitz continuous first-order Fréchet derivative in Banach spaces. This analysis avoids the usual application of Taylor expansion in convergence analysis and extends the applicability of the scheme by applying the technique based on the first-order derivative only. Also, our study provides the radius of convergence ball and computable error bounds along with the uniqueness of the solution. Furthermore, the generalization of this analysis using Hölder condition is provided. Various numerical tests confirm that our analysis produces better results and it is useful in solving such problems where previous methods can not be implemented.

【 授权许可】

Unknown