.png){kind=icon}
.png){kind=icon}
Return
Adaptive Parallel Methods for Polynomial Equations with Unknown Multiplicity
.png){kind=icon}
OA
AI
DOI：10.3390/a19010021.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
New two-step simultaneous iterative techniques are proposed for solving polynomial equations with multiple roots of unknown multiplicity. The developed schemes achieve a local convergence order of ten and address key limitations of existing solvers, namely their dependence on prior multiplicity information and their reduced efficiency when dealing with clustered or repeated roots. Root multiplicities are adaptively estimated within the iterative process, avoiding additional function evaluations beyond those required for parallel updates. The robustness and stability of the proposed methods are assessed using both random and distant initial guesses and validated on benchmark polynomials as well as nonlinear models from biomedical engineering. The numerical results show notable improvements in residual error, iteration count, CPU time, memory usage, and overall convergence rate compared with established classical techniques. These findings demonstrate that the proposed schemes provide reliable, high-order, and computationally efficient tools for solving challenging nonlinear problems in science and engineering.
Keywords:
polynomial equations
multiple roots
unknown multiplicity
simultaneous iterative methods
adaptive algorithms
theoretical local convergence
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
2.1
Papers:
631
Citations:
5.4K