Lagrange Interpolation, Newton Interpolation, Hermite Interpolation, Jacobi Iteration, Gauss Iteration, and Cholesky Decomposition Algorithm Package

This algorithm package contains multiple numerical methods including Lagrange interpolation, Newton interpolation, Hermite interpolation, Jacobi iteration, Gauss-Seidel iteration, Successive Over-Relaxation (SOR) iteration, and Cholesky decomposition. These algorithms are essential in numerical analysis for solving various mathematical problems such as linear systems and polynomial fitting. The implementation features optimized computational efficiency through vectorized operations (where applicable) and proper convergence checks for iterative methods. Lagrange interpolation constructs polynomials using basis functions, Newton interpolation employs divided differences for progressive polynomial building, while Hermite interpolation incorporates derivative information. The iterative methods (Jacobi, Gauss-Seidel, SOR) include convergence criteria monitoring, and Cholesky decomposition implements symmetric positive-definite matrix factorization. These algorithms enhance computational accuracy and efficiency, making them widely applicable in engineering, physics, and computer science domains for numerical computations and scientific simulations.