Column Pivoting Gaussian Elimination Method

This MATLAB implementation utilizes the column pivoting Gaussian elimination method to solve linear equation systems. Gaussian elimination is a fundamental linear algebra algorithm that solves linear equations by performing operations on the coefficient matrix. The column pivoting technique enhances numerical stability by preventing division by small pivot elements and reducing rounding errors. During algorithm implementation, we perform several matrix operations including elimination, row swapping for pivot selection, and back substitution. The MATLAB implementation leverages built-in functions to efficiently handle these operations: - Pivot selection: Identifying the maximum absolute value in each column to determine the optimal pivot element - Row swapping: Using MATLAB's matrix indexing to exchange rows when necessary - Elimination process: Implementing the elimination phase with proper scaling factors for numerical accuracy - Back substitution: Solving the upper triangular system from bottom to top Key MATLAB functions and techniques employed include matrix indexing for efficient row operations, vectorized computations for performance optimization, and proper handling of floating-point arithmetic to maintain precision throughout the solution process.