- My research
- NLA
- Parallel and HPC computing, GPU computing
- Machine learning, surrogate modeling, stochastic inversing, anomaly detection
- Cybersecurity
- Teaching team:
- Rajat Dwaraknath
- Ishani Karmarkar
- Chartsiri Jirachotkulthorn
- Style of class and what to expect
- This class will require some proof-writing
- What is numerical linear algebra?
- Example: difference between the existence of eigenvalues and eigenvectors and how to compute them
- A class on numerical methods covers:
- Algorithms to solve a mathematical problem
- Computational cost
- Many algorithms are approximate; what is the error? how can it be controlled? how can it be estimated?
- Roundoff errors and stability: how do small errors in the data and during the calculation affect the final result?
- There will be some computer programming, but this is not the main focus
- We won’t discuss applications in detail
- The focus is on the algorithms, computational cost, and error analysis
- Content of class
- Solving linear systems: Ax=b.
- QR factorization and least-squares: minx∥Ax−b∥.
- Eigendecomposition using direct methods: Ax=λx.
- Iterative methods and Krylov subspace; Conjugate Gradient, GMRES
- Canvas
- Survey
- Ed Discussion forum
- Rules of conduct on forum
- Be civil, considerate, and courteous
- Make sure not to post answers or partial answers to homework assignments
- Anonymous form to report issues and concerns
- Office hours posted on canvas
- Recitation sessions
- Main lectures on Wednesday and Friday; recitations on Monday
- Basic LA review
- Julia / Python quick overviews and getting started
- Programming languages
- Reading
- Required book: Darve and Wootters, Numerical Linear Algebra with Julia
- Optional books:
- Matrix Computations by Gene H. Golub and Charles F. Van Loan
- Numerical Linear Algebra by Lloyd N. Trefethen and David Bau III
- Applied numerical linear algebra by James W. Demmel
- Direct methods for sparse linear systems by Timothy A. Davis
- See searchworks.stanford.edu
- Grading; grades are curved to reach a typical distribution of As, Bs, and Cs.
- Homework 35%
- Midterm exam 1 15%
- Midterm exam 2 20%
- Final exam 30%
- Gradescope; the website will manage the regrade requests.
- Late policy
- 72 hours; 10% penalty
- Excused late submissions: requests must be submitted 24 hours before the deadline.
- Access and accommodations
- Office of Accessible Education (OAE)
- Share your letter with us
- Honor Code and Office of Community Standards
- Do not share answers with other students
- Do not let other students copy your answers
- Do not copy answers from previous years
- Do not copy answers from TAs or teaching staff
- Do not copy answers on the internet
- Do not post/share answers on the internet
- Answers must be your own