Hermite Interpolation Function Implementation in MATLAB

In MATLAB, there is no direct Hermite interpolation function available, necessitating the creation of a custom M-file to perform interpolation operations. The implementation requires inputting node data through three arrays: x0 (containing x-coordinates of known points), y0 (function values at these points), and y1 (derivative values at these points) for n nodes—crucially noting MATLAB's 1-based array indexing convention. The m interpolation points are provided via array x, with the output array y returning calculated function values for all m points. To achieve this, developers must create hermite.m containing the Hermite interpolation algorithm, typically implementing divided difference tables that incorporate both function and derivative values. The core algorithm involves constructing a piecewise cubic polynomial that matches both the function values and first derivatives at given nodes, ensuring C1 continuity. Key implementation steps include proper handling of repeated nodes for derivative conditions and efficient evaluation using Horner's method or direct polynomial calculation.