Matrix Analysis and Algorithms

This page contains lecture notes about numerical linear algebra which I wrote together with Andrew Stuart. The notes form the basis of the MA398 numerical linear algebra module at the university of Warwick.

Contents

• Vector and Matrix Analysis
  • Vector Norms and Inner Products
  • Eigenvalues and Eigenvectors
  • Dual Spaces
  • Matrix Norms
  • Structured Matrices
• Matrix Factorisations
  • Diagonalisation
  • Jordan Canonical Form
  • Singular Value Decomposition
  • QR Factorisation
  • LU Factorisation
  • Cholesky Factorisation
• Stability and Conditioning
  • Conditioning of SLE
  • Conditioning of LSQ
  • Conditioning of EVP
  • Stability of Algorithms
• Complexity of Algorithms
  • Computational Cost
  • Matrix-Matrix Multiplication
  • Fast Fourier Transform
  • Bidiagonal and Hessenberg Forms
• Systems of Linear Equations
  • Gaussian Elimination
  • Gaussian Elimination with Partial Pivoting
  • The QR Factorisation
• Iterative Methods
  • Linear Methods
  • The Jacobi Method
  • The Gauss-Seidel and SOR Methods
  • Nonlinear Methods
  • The Steepest Descent Method
  • The Conjugate Gradient Method
• Least Squares Problems
  • LSQ via Normal Equations
  • LSQ via QR factorisation
  • LSQ via SVD
• Eigenvalue Problems
  • The Power Method
  • Inverse Iteration
  • Rayleigh Quotient Iteration
  • Simultaneous Iteration
  • The QR Algorithm for Eigenvalues
  • Divide and Conquer for Symmetric Problems

Download

The script is available for download here.

• A.M. Stuart and J. Voss: Matrix Analysis and Algorithms. Lecture notes, 2009.
  preprint, more…

Copyright © 2009, Jochen Voss. All content on this website (including text, pictures, and any other original works), unless otherwise noted, is licensed under a Creative Commons Attribution-Share Alike 3.0 License. Last update: 2009-07-31.