Editing Iterative method (section)

==Attractive fixed points==
If an equation can be put into the form ''f''(''x'') = ''x'', and a solution '''x''' is an attractive [[fixed point (mathematics)|fixed point]] of the function ''f'', then one may begin with a point ''x''<sub>1</sub> in the [[basin of attraction]] of '''x''', and let ''x''<sub>''n''+1</sub> = ''f''(''x''<sub>''n''</sub>) for ''n''&nbsp;≥&nbsp;1, and the sequence {''x''<sub>''n''</sub>}<sub>''n''&nbsp;≥&nbsp;1</sub> will converge to the solution '''x'''. Here ''x''<sub>''n''</sub> is the ''n''th approximation or iteration of ''x'' and ''x''<sub>''n''+1</sub> is the next or ''n'' + 1 iteration of ''x''.  Alternately, superscripts in parentheses are often used in numerical methods, so as not to interfere with subscripts with other meanings.  (For example, ''x''<sup>(''n''+1)</sup> = ''f''(''x''<sup>(''n'')</sup>).) If the function ''f'' is [[continuously differentiable]], a sufficient condition for convergence is that the [[spectral radius]] of the derivative is strictly bounded by one in a neighborhood of the fixed point.  If this condition holds at the fixed point, then a sufficiently small neighborhood (basin of attraction) must exist.