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Session 5
Numerical Computation
Advanced Eigenvalue Computations
4.5 hours
Duration
8
Materials
6
Objectives
Session Overview
Sophisticated algorithms for eigenvalue problems including QR algorithm with shifts, Lanczos method, Arnoldi iteration, and specialized methods for large sparse matrices.
Learning Objectives
By the end of this session, you should be able to:
- Implement QR algorithm with single and double shifts for dense matrices
- Master Lanczos algorithm for symmetric eigenvalue problems
- Understand Arnoldi iteration for nonsymmetric eigenvalue computation
- Apply implicitly restarted Arnoldi method (IRAM) for large sparse problems
- Implement specialized methods for generalized eigenvalue problems
- Analyze convergence and computational efficiency of eigenvalue algorithms
Course Materials
Download materials for offline study and reference
Advanced Eigenvalue Algorithm Theory (75 pages)
Available material
QR Algorithm with Shift Implementation
Available material
Lanczos and Arnoldi Method Development
Available material
Implicitly Restarted Arnoldi Implementation
Available material
Generalized Eigenvalue Problem Solvers
Available material
Large Sparse Matrix Eigenvalue Applications
Available material
Performance Analysis and Optimization
Available material
Complete Eigenvalue Computation Package
Available material