Durand–Kerner method: Difference between revisions

Content deleted Content added
Variations: Find real roots of odd-degree polynomials.
Yobot (talk | contribs)
m Variations: WP:CHECKWIKI error fixes using AWB
Line 93:
as the degree of the polynomial increases.
 
If the coefficients are real and the polynomial has odd degree, then it must have at least one real root. To find this, use a real value of <i>''p</i>''<sub>0</sub> as the initial guess and make <i>''q</i>''<sub>0</sub> and <i>''r</i>''<sub>0</sub>, etc, [[complex conjugate]] pairs. Then the iteration will preserve these properties; that is, <i>''p</i>''<sub><i>''n</i>''</sub> will always be real, and <i>''q</i>''<sub><i>''n</i>''</sub> and <i>''r</i>''<sub><i>''n</i>''</sub>, etc, will always be conjugate. In this way, the <i>''p</i>''<sub><i>''n</i>''</sub> will converge to a real root <i>''P</i>''. Alternatively, make all of the initial guesses real; they will remain so.
 
== Example ==