We will discuss the following NLA topics

- Low-rank approximations.
- Rank-revealing factorizations.
- Randomized algorithms.
- Subset-based singular value decompositions.
- Preconditioning techniques.

Our main applications include large scale NLA, optimization, and large data analysis. Our course has a significant overlap, but is different from the topics course, Stat260/CompSci294 , "Randomized Algorithms for Matrices and Data", offered by Prof. Michael Mahoney in Fall 2013.

Office: Evans 861

Lectures: MF, 11:00AM-12:30PM, 891 Evans Hall.

Office Hours: TBA , or by appointment.

Phone: 642-3145

Email: mgu@math

There are no exams nor weekly homeworks. Course work will instead include literature research and presentation in related topics. Additionally, we will have two progamming projects, and one term paper, both to be done in groups of 2-3 students. This course will be structured in such a way that a successful term paper should be one that will be submitted for journal publication. We will discuss the following NLA topics

- Low-rank approximations.
- Rank-revealing factorizations.
- Randomized algorithms.
- Subset-based singular value decompositions.
- Preconditioning techniques.

- Strong Rank-revealing QR factorizations.
- CS Decomposition.
- Condition Numbers of Gaussian Random Matrices.
- Finding structure with randomness.

- Survey paper on randomized algorithms for matrices and data.
- Randomized Subspace Iteration.
- CUR matrix decompositions for improved data analysis .
- Improving CUR Matrix Decomposition and the Nystrom Approximation via Adaptive Sampling.