- Bau III, D., & Trefethen, L.N. (1997). Numerical Linear Algebra. Philadelphia, PA: Society for Industrial & Applied Mathematics. This is a book that focuses on numerical linear algebra. Required!
- Demmel, James, (1997). Applied Numerical Linear Algebra. Philadelphia, PA: Society for Industrial & Applied Mathematics.
- Additional material for more advanced topics will be announced
later in the semester.

A problem set will be assigned on Wednesday each week, which will be due in class on Wednesday next week. The problem sets appear at the bottom of this web-page.

Students can discuss problems with each other or seek tips from books, articles or online rescources. But it is wrong to simply copy from any source. See Penn Office of Student Conduct.

- The class meets on MonWed from 10:30 am to 12:00 pm in room 4C2 in
the
David
Rittenhouse Labs.

- My office hour will be Wednesdays 1:00 pm-2:00 pm or by appointment via email if you can not come during this time.
- My office in the Math Department is 4N63 DRL, tel. (215) 898-7844.
- My email: zwang423@math.upenn.edu. Send e-mail if you have a question or need to contact me.
- The grader is Hadi Elzayn. Office Hour: By appointment at DRL 1N1. His email: hads@sas.upenn.edu.

- Matrix operations
- Floating point arithmetic

- QR and least squares
- Norms, conditioning and stability
- Direct methods for systems of linear equations, including
- LU
- QR
- SVD factorizations
- Gaussian Elimination

- Iterative methods
- Krylov
- Arnoldi
- GMRES
- Lanczos

- Matrix eigenvalue problems
- Symmetric matrices
- Non-symmetric matrices, spectrum and pseudospectrum
- The Perron-Frobenius theorem

Additional topics taken from:

- Orthogonal polynomials and 3-term recurrence relations
- Numerical quadratures
- Numerical solution of PDEs

- Compression and randomized algorithms
- Discrete Fourier and wavelet transforms
- Linear programming

- This class will have its first meeting on Wednesday, August 30, 2017. Good references for the necessary background material are Linear Algebra by Peter Lax, Linear Algebra and Its Applications by Gilbert Strang, and Introduction to Matrix Analysis by Richard Bellman.

- Homework 1 . Due Sept. 13, 2017
- Homework 2 . Due Sept. 20, 2017.
- Homework 3 . Due Oct. 2, 2017.
- Matlab project 1 . Due Oct. 9, 2017. You might find it helpful to refer to the worksheets worksheet 1 and worksheet 2 due to Dr. Epstein.
- Homework 4 . Due Oct. 18, 2017.
- Homework 5 . Due Oct. 30, 2017.
- Homework 6 . Due Nov. 15, 2017.
- Homework 7 . Due Nov. 29, 2017.
- Final Project/Exam . Due Dec. 6, 2017.

- A link to A Randomized
Algorithm for the Decomposition of Matrices, by Martinsson, Roklin
and Tygert.

- A link to Randomized Algorithms for the low-rank Approximation of Matrices, by Liberty, Woolfe, Martinsson, Roklin and Tygert.
- A link to The Toda Lattice, Old and New, by Carlos Tomei
- A link to ON THE COMPRESSION OF LOW RANK MATRICES, by H. CHENG, Z. GIMBUTAS, P. G. MARTINSSON, AND V. ROKHLIN.
- A page discussing the QBX method for evaluation of layer potentials described in class.
- The PSEUDOSPECTRUM web-page of Mark Embree and Nick Trefethen.