MATLAB Implementation of Cubic Spline Interpolation

In the field of interpolation algorithms, there exists a method known as "cubic spline interpolation." This approach is widely recognized as an excellent interpolation technique due to its ability to closely approximate function curves with high precision. The algorithm constructs the interpolation curve by dividing the domain into small subintervals, with each subinterval represented by a distinct cubic polynomial. These cubic curves are smoothly connected at the knots (data points) by enforcing continuity conditions for the function value, first derivative, and second derivative. Key implementation aspects in MATLAB typically involve: - Using the `spline` function for built-in cubic spline interpolation - Alternatively, implementing custom algorithms using `csape` for different boundary conditions - Solving tridiagonal systems of equations to determine polynomial coefficients - Ensuring C² continuity (continuous second derivatives) at interior points This method produces smoother results compared to other interpolation algorithms, making it particularly effective for capturing the true shape of underlying curves. The natural cubic spline variant minimizes curvature while fitting all data points exactly. If you are seeking a reliable interpolation algorithm for smooth curve fitting, cubic spline interpolation is certainly worth considering for your MATLAB applications in numerical analysis, computer graphics, or engineering simulations.