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Session 13
Numerical Methods

Eigenvalue Problems and Matrix Computations

4 hours
Duration
8
Materials
6
Objectives
Session Overview

Numerical methods for computing eigenvalues and eigenvectors including power method, QR algorithm, and Jacobi method. Applications to vibration analysis and principal component analysis.

Learning Objectives
By the end of this session, you should be able to:
  • Implement power method and inverse power method for dominant eigenvalues
  • Understand deflation techniques for multiple eigenvalue computation
  • Master QR algorithm with shifts for complete eigenvalue computation
  • Apply Jacobi method for symmetric matrix eigenproblems
  • Understand Gershgorin circle theorem for eigenvalue localization
  • Apply eigenvalue methods to engineering problems and data analysis
Course Materials
Download materials for offline study and reference
Eigenvalue Theory and Matrix Analysis (48 pages)
Available material
Power Method Implementation and Convergence Analysis
Available material
QR Algorithm with Shift Strategies
Available material
Jacobi Method for Symmetric Matrices
Available material
Gershgorin Circles and Eigenvalue Bounds
Available material
Vibration Analysis Application Examples
Available material
Principal Component Analysis Implementation
Available material
Comprehensive Eigenvalue Solver Project
Available material