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General Local Convergence Theorems about the Picard Iteration in Arbitrary Normed Fields with Applications to Super–Halley Method for Multiple Polynomial Zeros
| Content Provider | MDPI |
|---|---|
| Author | Ivanov, Stoil I. |
| Copyright Year | 2020 |
| Description | In this paper, we prove two general convergence theorems with error estimates that give sufficient conditions to guarantee the local convergence of the Picard iteration in arbitrary normed fields. Thus, we provide a unified approach for investigating the local convergence of Picard-type iterative methods for simple and multiple roots of nonlinear equations. As an application, we prove two new convergence theorems with a priori and a posteriori error estimates about the Super-Halley method for multiple polynomial zeros. |
| Starting Page | 1599 |
| e-ISSN | 22277390 |
| DOI | 10.3390/math8091599 |
| Journal | Mathematics |
| Issue Number | 9 |
| Volume Number | 8 |
| Language | English |
| Publisher | MDPI |
| Publisher Date | 2020-09-17 |
| Access Restriction | Open |
| Subject Keyword | Mathematics Automotive Engineering Iterative Methods Local Convergence Error Estimates Normed Fields Super-halley Method Polynomial Zeros Multiple Zeros |
| Content Type | Text |
| Resource Type | Article |
