Topics that the Course will Cover
These are the topics that I plan to cover, not necessarily in this order:
- Least Squares and the QR factorization
- Linear equations and triangular factorization (LU, Cholesky)
- Matrix multiplication and performance issues (work, communication, parallelism)
- SVD, projections, orthogonality (that is, missing mathematical background)
- Floating-point arithmetic, conditioning, and stability
- Fast Fourier Transform (FFT)
- Sparse factorizations
- Dense Eigensolvers
- Iterative methods for linear equations, least squares, and eigenvalues; preconditioning
- Randomized algorithms in Numerical Linear Algebra
- A least squares solver using Givens Rotations. Due on March 17, but please solve part 6 by March 10.
- Fast matrix multiplication. Due on April 7.
- Image compression through the SVD. Due on May 5.
- Fixed point arithmetic and stability of fixed-point algorithms (due on May 26)
- The Jacobi Eigensolver (due on June 16)