Syllabus

MACS/MAGN 551
Numerical Linear Algebra
Spring 1995, 206 Berthoud Hall 11:00-11:50 MWF

Instructor: Erik Van Vleck
Office: Stratton 216
Office Hours: MW 10:00-11:00
Text: Watkins, Fundamentals of Matrix Computations

Grades:
Various Individual and Group Assignments (40)
2 Midterm Exams (40)
1 Final Individual Project (20)

Important Dates:
Midterm 1 (in class) on Wednesday, February 15, 1995
Midterm 2 (in class) on Wednesday, March 29, 1995
Final Project due Tuesday, May 2, 1995

All assignments due at the beginning of class
NO LATE ASSIGNMENTS ACCEPTED UNDER ANY CIRCUMSTANCES

Supplementary material:

Golub and Van Loan, ``Matrix Computations''.

Demmel, ``Numerical Linear Algebra''.

Linpack User's Guide.

Lapack User's Guide.



Syllabus

MACS/MAGN 551
Computational Linear Algebra

Spring 1995, 206 Berthoud Hall, 11:00-11:50 MWF

Instructor: Erik Van Vleck
Office: Stratton 216

Text: Watkins, Fundamentals of Matrix Computations

Outline

Gaussian Elimination
- Cholesky decomposition
- LU decomposition
- Banded systems
- Pivoting

Sensitivity of Linear Systems
- Matrix and Vector Norms
- Conditioning
- Scaling
- Iterative Refinement

Least-Squares Problems
- Orthogonal Matrices
- Gram-Schmidt process
- Sensitivity in Least-Squares

Eigenvalues and Eigenvectors
- Basic Properties
- Power Method and Extensions
- QR Algorithm
- Invariant Subspaces
- Lanczos Algorithm

The Singular Value Decomposition
- Least-Squares
- Angles and Distances between Subspaces

Special Topics
- Iterative methods (including Krylov subspace methods)
- Multigrid methods
- Domain Decomposition methods