Self-Implemented Cubic Spline Interpolation Function with Custom Programming

I have developed the source code for a cubic spline interpolation function and applied this implementation to solve specific practical problems. It's worth noting that cubic spline interpolation finds applications in various domains such as image processing, signal processing, and more. During the programming process, I conducted in-depth research into the underlying principles and mathematical properties of spline interpolation to ensure algorithmic accuracy and computational reliability. The implementation employs key techniques including tridiagonal matrix solving for efficient coefficient calculation and boundary condition handling (natural, clamped, or periodic endpoints). Furthermore, I integrated optimization methods to enhance computational efficiency, such as matrix decomposition techniques (LU decomposition) for solving linear systems and parallel computing approaches for large-scale datasets. The implementation features functions for calculating spline coefficients, evaluating interpolated values at arbitrary points, and handling different boundary conditions. Overall, I consider cubic spline interpolation to be an exceptionally valuable mathematical tool that effectively addresses numerous real-world engineering challenges through robust numerical implementation.