Home » Teaching » Algorithms for High-Performance Computing

Algorithms for High-Performance Computing

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

Homework Assignments

  1. A least squares solver using Givens Rotations. Due on March 17, but please solve part 6 by March 10.
  2. Fast matrix multiplication. Due on April 7.
  3. Image compression through the SVD. Due on May 5.
  4. Fixed point arithmetic and stability of fixed-point algorithms (due on May 26)
  5. The Jacobi Eigensolver (due on June 16)
%d bloggers like this: