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Session 5
Numerical Methods
Iterative Methods for Linear Systems
3.5 hours
Duration
8
Materials
6
Objectives
Session Overview
Detailed study of iterative methods including Jacobi, Gauss-Seidel, and SOR methods. Convergence analysis, spectral radius, and preconditioning techniques for large sparse systems.
Learning Objectives
By the end of this session, you should be able to:
- Implement Jacobi and Gauss-Seidel methods with matrix splitting theory
- Master Successive Over-Relaxation (SOR) method and optimal relaxation parameter
- Analyze convergence conditions using spectral radius and diagonal dominance
- Apply iterative methods to large sparse systems from engineering applications
- Understand preconditioning techniques for accelerating convergence
- Compare direct vs iterative methods for different problem types and sizes
Course Materials
Download materials for offline study and reference
Matrix Splitting Theory and Convergence Proofs (38 pages)
Available material
SOR Method Optimization Analysis
Available material
Sparse Matrix Applications in Engineering
Available material
Preconditioning Techniques Guide
Available material
Convergence Criteria and Stopping Rules
Available material
Large-Scale Problem Examples
Available material
Performance Comparison Studies
Available material
Programming Project: Iterative Solver Suite
Available material