Cubic spline interpolation is a piecewise interpolation method that fits a cubic polynomial between each pair of data points. The cubic spline interpolation is a popular method in numerical analysis because it is simple and efficient. In this lab, you will implement the cubic spline interpolation algorithm and apply it to interpolate a set of data points.

Numerical integration is a method for approximating the definite integral of a function. It is a fundamental algorithm in numerical analysis and is used in many applications. In this lab, you will implement the Trapezoidal rule、Simpson's rule and Romberg integration algorithm and apply them to approximate the definite integral of a function.

Gaussian elimination is a method for solving a system of linear equations. It is a fundamental algorithm in numerical analysis and is used in many applications. In this lab, you will implement the Gaussian elimination algorithm and apply it to solve a system of linear equations.

Iterative methods are a class of algorithms for solving a system of linear equations. They are used when the system is too large to be solved by direct methods such as Gaussian elimination. In this lab, you will implement the Jacobi method、Gauss-Seidel method and Successive Over-Relaxation method and apply them to solve a system of linear equations.