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  • Appendix A - Polynomial Interpolation

  • Bengt Fornberg, University of Colorado Boulder
  • Book:
    High-Accuracy Finite Difference Methods
    Published online:
    16 May 2025
    Print publication:
    05 June 2025, pp 155-158

  • Summary

    Polynomial interpolation is one of the most fundamental computational procedures, underlying a large number of more specialized numerical methods. With N distinct nodes in 1-D together with associated data values, there is a unique interpolating polynomial of degree N-1. In this brief appendix, we summarize some different ways to arrive at and then to represent this polynomial. There are also different error formulas available (measuring the difference between a smooth function and its polynomial interpolant). One particular way to formulate this difference, in the form of a complex plane contour integral, provides the key to understanding many features of polynomial interpolants (such as the Runge phenomenon, often causing violent oscillations near interval end points).