Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2509.20897 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909805858258944 |
|---|---|
| author | Foo, Wei Guo Tan, Chik How |
| author_facet | Foo, Wei Guo Tan, Chik How |
| contents | Root-finding method is an iterative process that constructs a sequence converging to a solution of an equation. Householder's method is a higher-order method that requires higher order derivatives of the reciprocal of a function and has disadvantages. Firstly, symbolic computations can take a long time, and numerical methods to differentiate a function can accumulate errors. Secondly, the convergence factor existing in the literature is a rough estimate. In this paper, we propose a higher-order root-finding method using only Taylor expansion of a function. It has lower computational complexity with explicit convergence factor, and can be used to numerically implement Householder's method. As an application, we apply the proposed method to compute pre-images of $q$-ary entropy functions, commonly seen in coding theory. Finally, we study basins of attraction using the proposed method and compare them with other root-finding methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20897 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-Order Root-Finding Algorithm and its Applications Foo, Wei Guo Tan, Chik How Numerical Analysis Information Theory Dynamical Systems 65H05, 94-08 Root-finding method is an iterative process that constructs a sequence converging to a solution of an equation. Householder's method is a higher-order method that requires higher order derivatives of the reciprocal of a function and has disadvantages. Firstly, symbolic computations can take a long time, and numerical methods to differentiate a function can accumulate errors. Secondly, the convergence factor existing in the literature is a rough estimate. In this paper, we propose a higher-order root-finding method using only Taylor expansion of a function. It has lower computational complexity with explicit convergence factor, and can be used to numerically implement Householder's method. As an application, we apply the proposed method to compute pre-images of $q$-ary entropy functions, commonly seen in coding theory. Finally, we study basins of attraction using the proposed method and compare them with other root-finding methods. |
| title | Higher-Order Root-Finding Algorithm and its Applications |
| topic | Numerical Analysis Information Theory Dynamical Systems 65H05, 94-08 |
| url | https://arxiv.org/abs/2509.20897 |