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Session 4
Numerical Computation

Krylov Subspace Methods and Conjugate Gradient

4.5 hours
Duration
8
Materials
6
Objectives
Session Overview

Advanced iterative methods based on Krylov subspaces including conjugate gradient, GMRES, and BiCGSTAB methods. Preconditioning techniques and convergence acceleration.

Learning Objectives
By the end of this session, you should be able to:
  • Understand Krylov subspace theory and its applications to linear systems
  • Implement conjugate gradient method with optimal convergence properties
  • Master GMRES method for nonsymmetric linear systems
  • Apply BiCGSTAB and other Krylov methods for various matrix types
  • Design and implement effective preconditioning strategies
  • Analyze convergence rates and computational complexity of Krylov methods
Course Materials
Download materials for offline study and reference
Krylov Subspace Theory and Methods (70 pages)
Available material
Conjugate Gradient Implementation and Analysis
Available material
GMRES and BiCGSTAB Algorithm Development
Available material
Preconditioning Techniques and Strategies
Available material
Convergence Analysis and Rate Estimation
Available material
Large-Scale Linear System Applications
Available material
Performance Optimization and Parallelization
Available material
Comprehensive Krylov Solver Library
Available material