## Project Description

The project takes the place of what would have been the last three homework assignments for the course. You can work in groups of two or three. Pick one of the problems that we are learning about, and take it further—to numerical examples, to applications, to testing a solution algorithm, or certainly to computations (using any language). Submit a short proposal just before or just after Spring Break. The project is due at the end of the last class.

## Topic Ideas

- SVD Applications to PCA
- Comparison of Algorithms
- Applications to Random Matrices
- Least Squares Comparisons of 4 Ways: Speed and Accuracy
- Comparison with Gradient Algorithms
- Sparse Solutions Using l_1
- Basis Pursuit and Other l_1 Optimizations Matrix Completion
- Gradient Descent and Stochastic Gradient Descent
- Acceleration Methods
- Learning Weights in a Neural Net
- Many Many Parameters—which Solution is Found by Descent?
- Low Rank Approximations
- Basic Applications