An Improved Second-Order Lagrange Interpolation Function

Lagrange interpolation is widely used in signal processing; however, high-order interpolation is affected by Runge phenomenon and the inflexible basis function construction. In this paper, an improved second-order Lagrange interpolation function is proposed, which uses a combination of piecewise second-order Lagrange interpolation results for interpolation. Compared with other low-order polynomial interpolation, the improved second-order Lagrange interpolation has a smaller root mean square error and can achieve an accuracy equivalent to that of a high-order Lagrange interpolation. Moreover, the improved second-order Lagrange interpolation is based on second-order interpolation without changing the interpolation basis function, which increases the flexibility of the algorithm.