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Session 2
Numerical Computation

Matrix Norms, Condition Numbers, and Sensitivity Analysis

4 hours
Duration
8
Materials
6
Objectives
Session Overview

Advanced study of matrix norms, condition number computation, and sensitivity analysis for linear systems. Perturbation theory and backward error analysis.

Learning Objectives
By the end of this session, you should be able to:
  • Compute and analyze vector and matrix norms (1, 2, Frobenius, infinity norms)
  • Master condition number computation and interpretation for linear systems
  • Understand perturbation theory for linear algebraic equations
  • Apply backward error analysis to assess algorithm stability
  • Implement efficient condition number estimation algorithms
  • Analyze sensitivity of eigenvalue problems to perturbations
Course Materials
Download materials for offline study and reference
Matrix Analysis and Perturbation Theory (55 pages)
Available material
Condition Number Computation Algorithms
Available material
Backward Error Analysis Framework
Available material
Sensitivity Analysis Case Studies
Available material
Efficient Norm and Condition Estimation Code
Available material
Linear System Perturbation Examples
Available material
Eigenvalue Sensitivity Analysis
Available material
Numerical Stability Assessment Tools
Available material