Lagrange Polynomial Interpolation, Gaussian Elimination for Solving Equations, Least Squares Fitting, Composite Trapezoidal Rule for Numerical Integration

This article demonstrates the implementation of crucial numerical computation methods using MATLAB programming. The featured algorithms include Lagrange Polynomial Interpolation for function approximation, Gaussian Elimination for solving systems of linear equations, Least Squares method for data fitting, and Composite Trapezoidal Rule for numerical integration. These methods are widely applied in scientific and engineering fields, providing powerful tools for mathematical understanding and practical problem-solving. The MATLAB implementations involve key programming aspects such as handling polynomial basis functions in Lagrange interpolation, matrix manipulation in Gaussian elimination, normal equation solving in least squares fitting, and iterative sum calculations in composite integration. Through coding these algorithms, developers can gain deeper insights into their mathematical principles while enhancing both programming skills and numerical analysis capabilities.