Matrix Analysis and Algorithms
By Jochen Voss, last updated 2011-08-31
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:pdf, more…
Copyright © 2011 Jochen Voss.
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