CS475/CS675 - Goals
Objectives
Numerical linear algebra is a basic part of many problems in
scientific computation. This course provides an overview of
algorithms and numerical linear 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 major topics:
- solving special linear systems,
- least squares problems,
- eigenvalue problems, and
- singular value decomposition.
Outline
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:
- Bidiagonalization.
- Search engine.