# Vandermonde interpolation approach

The Vandermonde approach for interpolation^{} is when we wish to determine the interpolating polynomial $p(x)={a}_{0}+{a}_{1}x+{a}_{2}{x}^{2}+\mathrm{\dots}+{a}_{n}{x}^{n}$ for the $n+1$ points $({x}_{i},{y}_{i})$, $i=0,1,\mathrm{\dots},n$ by forming the equations ${y}_{i}={a}_{0}+{a}_{1}{x}_{i}+{a}_{2}{x}_{2}^{2}+\mathrm{\dots}+{a}_{n}{x}_{n}^{n}$ for $i=0,1,\mathrm{\dots},n$, and solving for the unknown coefficients ${a}_{0},{a}_{1},\mathrm{\dots},{a}_{n}$.

The system of equations can be written by using matrices $Y=XA$ where $X$ is a Vandermonde matrix^{}.

Title | Vandermonde interpolation approach |
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Canonical name | VandermondeInterpolationApproach |

Date of creation | 2013-03-22 14:19:56 |

Last modified on | 2013-03-22 14:19:56 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 8 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 65D05 |

Classification | msc 41A05 |