A Note on Polynomial Interpolation

The Neville's algorithm and the Aitken's algorithm are successively linear interpolation approach to high degree Lagrangian interpolation. This note proposes a new approach with iteratively quadratic interpolation to high degree Lagrangian interpolation. The new algorithm here is cheaper (about 20% cheaper) than the Neville's algorithm. Several functions were tested. Numerical experiments coincide with the theoretical analysis. The combination of linear approach and quadratic approach is considered too.

Keywords:

• Aitken's Algorithm
• Neville's Algorithm
• Lagrangian Interpolation
• Successively Quadratic Interpolation
• Successively Linear Interpolation
• Polynomial Interpolation
• Parallel Computation