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Session 3
Numerical Computation

Advanced Matrix Factorizations: QR and SVD

4.5 hours
Duration
8
Materials
6
Objectives
Session Overview

Comprehensive treatment of QR decomposition methods, Singular Value Decomposition, and their applications in least squares, data analysis, and numerical rank determination.

Learning Objectives
By the end of this session, you should be able to:
  • Implement QR factorization using Householder reflections and Givens rotations
  • Master Gram-Schmidt process and its modified version for better numerical stability
  • Understand SVD computation using bidiagonalization and QR iteration
  • Apply QR and SVD to least squares problems and pseudoinverse computation
  • Use SVD for low-rank approximation and data compression
  • Implement numerical rank determination using SVD
Course Materials
Download materials for offline study and reference
Matrix Factorization Theory and Algorithms (65 pages)
Available material
Householder and Givens Rotation Implementations
Available material
SVD Algorithm Development and Optimization
Available material
Least Squares Applications and Case Studies
Available material
Low-rank Approximation and Data Compression Examples
Available material
Numerical Rank and Matrix Approximation
Available material
High-Performance Matrix Computation Techniques
Available material
Comprehensive Factorization Software Package
Available material