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Mjpnijmeijer (talk | contribs) ←Created page with '{{User sandbox}} <!-- EDIT BELOW THIS LINE --> == Sidi's method == Sidi's method is a root-finding algorithm, i.e. a numerical method for solving equations ...' |
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The estimate ''x''<sub>''n''+''k''+1</sub> is calculated as follows in the ''n''-th iteration. A polynomial ''p'' <sub>''n'', ''k'' </sub> (''x'') of degree ''k'' is fitted to the ''k'' + 1 points (''x''<sub>''n''</sub>, ''f''(''x''<sub>''n''</sub>)), …, (''x''<sub>''n''+''k''</sub>, ''f''(''x''<sub>''n''+''k''</sub>)). The next approximation ''x''<sub>''n''+''k''+1 </sub> of α is calculated as
:<math> x_{n+k+1} = x_{n+k} - \frac{f(x_{n+k})}{p_{n,k}'(x_{n+k})} </math>
with ''p’ '' <sub>''n'',''k''</sub>(''x''<sub>''n''+''k''</sub>) the derivative of ''p'' <sub>''n'',''k''</sub> at ''x''<sub>''n''+''k''</sub>.
== References ==
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