An improved computation of component centers in the degree-\(n\) bifurcation set (Q1847588)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: An improved computation of component centers in the degree-\(n\) bifurcation set |
scientific article; zbMATH DE number 1836016
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An improved computation of component centers in the degree-\(n\) bifurcation set |
scientific article; zbMATH DE number 1836016 |
Statements
An improved computation of component centers in the degree-\(n\) bifurcation set (English)
0 references
4 June 2003
0 references
The governing equation locating component centers in the degree-\(n\) bifurcation set is a polynomial with very high degree, and its root-finding lacks numerical accuracy. The equation is transformed to have its degree reduced by a factor \((n-1)\). Newton's method applied to the transformed equation improves the accuracy with properly chosen initial values. The numerical implementation is done with Maple V using a large number of effective digits. Many cases are studied for \(2 \leq n \leq 25\). Remarkably improved results are obtained.
0 references
bifurcation
0 references
component center
0 references
degree-n bifurcation set
0 references
Mandelbrot set
0 references
Newton's method
0 references
polynomial root-finding
0 references
0.96049297
0 references
0 references
0.8671345
0 references
0.85914505
0 references
0.8557452
0 references
0.85479206
0 references
0.8490896
0 references
0.84842587
0 references
