Maps for global separation of roots
arXiv:1511.077161 citationsh-index: 3
Originality Synthesis-oriented
AI Analysis
This is an incremental theoretical contribution for numerical analysts working on root-finding algorithms.
The paper introduces quasi-step maps to globally separate fixed points of iteration maps in an interval, providing worked examples for Newton and Halley methods.
Two simple predicates are adopted and certain real-valued piecewise continuous functions are constructed from them. This type of maps will be called quasi-step maps and aim to separate the fixed points of an iteration map in an interval. The main properties of these maps are studied. Several worked examples are given where appropriate quasi-step maps for Newton and Halley iteration maps illustrate the main features of quasi-step maps as tools for global separation of roots.