Numerical Linear Algebra
Learning Objective:When we reach the end of the class, you should be able to:
- Understand the algorithms underlying matrix computations software for dense matrices
- Be able to implement basic versions of these algorithms
- Understand the difference between iterative methods for linear systems and direct methods
- Be able to implement iterative methods for large scale problems
- Appreciate the variety of applications of matrix computations
This course is an in-depth study of numerical linear algebra and the matrix computations that arise in solving linear systems, least squares problems, and eigenvalue problems for dense and sparse matrices. It will cover many of the fundamental algorithms such as the LU decomposition, the Cholesky decomposition, the conjugate gradient method, and the GMRES method. The course is designed for those who wish to use matrix computations in their own research and especially those in applied engineering and science.
- Linear Least Squares, Linear Systems, Singular Values, Eigenvalues, Sparse Matrices, Gradient descent, power method
- Finite Termination
- Coordinate fixing algorithms like -> Cholesky
- LU with pivoting
- QR factorization Conditioning & Stability
- How to choose algorithms? Advanced Problems
- Sequences of linear systems
- Generalized eigenvalue problems Krylov Methods
- Arnoldi, Lanczos Eigenvalue algorithms
- All eigenvalues
- Some eigenvalues
Prerequisites:A bachelor degree in computer science or an equivalent field.
This class is an in-depth graduate lecture class. You (the student) should have taken a mathematical course on linear algebra that covers vector spaces as well as a numerical analysis course that covers computer implementations of numerical algorithms.
Applied / Theory:40 / 60
Web Content:Syllabus, schedule, readings, references, homework assignments, and message board. Piazza to support course
Homework:Frequent quizzes and homeworks.
Exams:One midterm and a final exam.
Textbooks:Official textbook information is now listed in the Schedule of Classes. NOTE: Textbook information is subject to be changed at any time at the discretion of the faculty member. If you have questions or concerns please contact the academic department.
Tentative--Matrix Computations. Gene H. Golub and Charles van Loan. 4th Edition, Johns Hopkins University Press. Numerical Linear Algebra. Lloyd N. Trefethen and David Bau. ISBN: 9781421407944 SIAM.