CS475/CM375 - Goals
Numerical linear algebra is a basic part of many problems in scientific
computation. This course provides an overview of algorithms and
algebra techniques to solve common problems that arise in many areas
such as image processing, search engines, natural language processing,
computational finance, aircraft design and artificial intelligence. The
course is structured around four
- solving special linear systems,
- least squares problems,
- eigenvalue problems, and
- singular value decomposition.
The topics we will cover include:
- Solving Linear Systems:
- LU factorization, Cholesky factorization.
- Special matrices: tridiagonal, band, general sparse matrices.
- Iterative methods, conjugate gradient, convergence.
- Least Squares Problems:
- Pseudo inverse.
- QR factorization.
- Householder transform,
- Givens rotation.
- Eigenvalue Problems:
- Eigenvalues and eigenvectors.
- Characteristic polynomials.
- Schur form.
- Power iteration, inverse iteration.
- QR method.
- Jacobi, divide-and-conquer.
- Singular Value Decomposition:
- Search engine.