Iterative Methods for Solving Linear Systems of Equations

In the MATLAB algorithm collection, iterative methods for solving linear systems of equations represent a fundamental mathematical approach. Solving linear equation systems is a classical computational problem typically involving multiple unknowns and equations. Through iterative techniques, solutions can be progressively approximated to achieve increasingly accurate results. MATLAB provides various iterative methods for solving linear systems, including Jacobi iteration, Gauss-Seidel iteration, and the Conjugate Gradient method. Each algorithm employs distinct implementation strategies: - Jacobi iteration updates each variable simultaneously using previous iteration values - Gauss-Seidel method utilizes immediately computed new values for subsequent calculations - Conjugate Gradient method optimizes convergence for symmetric positive-definite matrices While these algorithms differ in specific implementation approaches, they share the common objective of iteratively approximating solutions to linear equation systems. Key MATLAB functions for implementation typically involve matrix operations, convergence checks, and iteration controls using while or for loops with precision thresholds. Therefore, within MATLAB's standard algorithm collection, iterative methods for solving linear equations constitute a critically important functionality for numerical computing and engineering applications.