Kategorie:Lagrange'sches Interpolationspolynom

Lagrange'sches Interpolationspolynom[Bearbeiten | Quelltext bearbeiten]

${\displaystyle p(x)=y_{0}L_{0}(x)+y_{1}L_{1}(x)+\ldots +y_{n}L_{n}(x)}$

wobei ${\displaystyle L_{i}(x)=\prod _{j\not =i}{\frac {x-x_{j}}{x_{i}-x_{j}}}={\frac {(x-x_{0})\ldots (x-x_{i-1})(x-x_{i+1})\ldots (x-x_{n})}{(x_{i}-x_{0})\ldots (x_{i}-x_{i-1})(x_{i}-x_{i+1})\ldots (x_{i}-x_{n})}}}$