Math 189M: Numerical Linear Algebra

This course is meant to introduce you to the analysis and computer implementation of basic numerical techniques for problems coming from linear algebra.  You will learn to explain how, why, and when these techniques can be expected to work and will lay a solid foundation for further study in numerical analysis and scientific computing.  Topics covered will include solution of linear equations, least-squares, matrix factorization, eigenvalue problems, and applications.

Resources

There is no required textbook for this course.  My lectures will be primarily based upon Fundamentals of Numerical Computation by Driscoll and Braun, Numerical Linear Algebra with Julia by Darve and Wootters, and Numerical Linear Algebra by Trefethen and Bau.  Applied Numerical Linear Algebra by Demmel is another excellent reference.

Tentative Course Schedule

Week Lecture Topic
1 1 Floating point numbers, Conditioning
Slides
2 Algorithms, Stability, Linear algebra review
Slides
2 3 Polynomial interpolation, Linear systems
Slides
4 LU factorization, Row pivoting
Slides
3 5 Vector and matrix norms, Fixed-point and splitting methods
Slides