next up previous contents index
Next: List of Tables Up: book Previous: List of Direct Algorithms   Contents   Index


List of Figures

  1. Damped, vibrating mass-spring system.
  2. Residual estimates, L-shaped membrane matrix.
  3. Ritz values, L-shaped membrane matrix.
  4. Residual estimates, Medline SVD matrix
  5. Residual estimates, shift-and-invert L-shaped membrane matrix.
  6. Jacobi-Davidson for exterior eigenvalues with several strategies for solving the correction equation.
  7. Jacobi-Davidson for exterior eigenvalues (top) and interior eigenvalues (bottom). The correction equations have been solved with 5 steps of plain GMRES (left) and with 5 steps of preconditioned GMRES (right).
  8. Residual estimates, Lanczos with shift-and-invert, L-membrane 9-point finite difference approximation.
  9. Relative accuracy of eigenvalues computed with and without direct balancing for the QH$768$ and TOLOSA matrices.
  10. Relative accuracy of eigenvalues computed with and without Krylov balancing for the QH$768$ and TOLOSA matrices.
  11. Comparison of the relative accuracy of the largest and smallest (in magnitude) eigenvalues of the QH$768$ matrix, with different Krylov-based balancing algorithms, using the default settings of five iterations and a cutoff value of $10^{-8}$.
  12. Comparison of the relative accuracy of the largest and smallest (in magnitude) eigenvalues of the TOLOSA matrix, with different Krylov-based balancing algorithms, using the default settings of five iterations and a cutoff value of $10^{-8}$.
  13. Jacobi-Davidson for exterior eigenvalues (left side) and interior eigenvalues (right side).
  14. Convergence history for BFW$782$.
  15. Procrustes problem
  16. Jordan problem
  17. Trace minimization problem
  18. LDA toy problem
  19. Simultaneous Schur problem
  20. Simultaneous diagonalization problem
  21. The unconstrained differential of $F(Y)$ can be projected to the tangent space to obtain the covariant gradient, $G$, of $F$.
  22. In a flat space, comparing vectors at nearby points is not problematic since all vectors lie in the same tangent space.
  23. In a curved manifold, comparing vectors at nearby points can result in vectors which do not lie in the tangent space.
  24. Profile of a nonsymmetric skyline or variable-band matrix.
  25. Logarithmic plots of residual norms of the inexact rational Krylov method for the Olmstead problem. The circles denote $\Vert f_j\Vert$ and the bullets $\Vert r_j\Vert$.
  26. Conjugate gradient versus steepest ascent, $\delta _1 / \delta _0=10$
  27. Conjugate gradient versus steepest ascent, $\delta _1 / \delta _0=100$
  28. Conjugate gradient versus steepest ascent, $\delta _1 / \delta _0=1000$



Susan Blackford 2000-11-20