4610 Project List

here are six suitable projects. We will talk about who is doing what on Monday.
  1. Tiled Jacobi eigenvalue computations. We will talk about the motivation for these projects on Monday.
    1. Basic Givens and Householder Testing. For matrices of size 2x2, 4x4, 8x8, 16x16, 32x32, 64x64, explore the convergence of different sweep patterns and zeroing rotations and reflections. This is two projects which require cooperation!
      1. The rotations to be tested are 2x2 Givens (similarity zeroer and column zeroer), 4x4 Givens column zeroer, 8x8 Givens column zeroer and blocked versions of these.
      2. Householder reflections (of numerous sizes and blockings).
    2. 4x4 Givens Rotaion implementation and testing. This is again two projects that require cooperation.
      1. Implement the 4x4 Givens similarity rotation described in a paper (with the subsidiary 3x3 SVD done by Mma) and explore the convergence of this rotation in diagonalizing 8x8, 16x16, 32x32, and 64x64 matrices.
      2. Implement and test readily computable approximations for left and right singular vectors associated with the largest singular value of a 3x3 matrix. Test the interaction of the approximations with the 4x4 Givens similarity block diagonalizer.
  2. Code and explore the convergence behavior of the Conjugate Gradient Algorithm in the text for suitable matrices from Matrix Marketplace.
  3. Code and explore the convergence behavior of the Arnoldi Eigenvalue algorithm in the text for suitable matrices from Matrix Marketplace.