- Damped, vibrating mass-spring system.
- Residual estimates, L-shaped membrane matrix.
- Ritz values, L-shaped membrane matrix.
- Residual estimates, Medline SVD matrix
- Residual estimates, shift-and-invert L-shaped membrane matrix.
- Jacobi-Davidson for exterior eigenvalues with several strategies for solving the correction equation.
- 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).
- Residual estimates, Lanczos with shift-and-invert, L-membrane 9-point finite difference approximation.
- Relative accuracy of eigenvalues computed with and without direct balancing for the QH and TOLOSA matrices.
- Relative accuracy of eigenvalues computed with and without Krylov balancing for the QH and TOLOSA matrices.
- Comparison of the relative accuracy of the largest and smallest (in magnitude) eigenvalues of the QH matrix, with different Krylov-based balancing algorithms, using the default settings of five iterations and a cutoff value of .
- 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 .
- Jacobi-Davidson for exterior eigenvalues (left side) and interior eigenvalues (right side).
- Convergence history for BFW.
- Procrustes problem
- Jordan problem
- Trace minimization problem
- LDA toy problem
- Simultaneous Schur problem
- Simultaneous diagonalization problem
- The unconstrained differential of can be projected to the tangent space to obtain the covariant gradient, , of .
- In a flat space, comparing vectors at nearby points is not problematic since all vectors lie in the same tangent space.
- In a curved manifold, comparing vectors at nearby points can result in vectors which do not lie in the tangent space.
- Profile of a nonsymmetric skyline or variable-band matrix.
- Logarithmic plots of residual norms of the inexact rational Krylov method for the Olmstead problem. The circles denote and the bullets .
- Conjugate gradient versus steepest ascent,
- Conjugate gradient versus steepest ascent,
- Conjugate gradient versus steepest ascent,

Susan Blackford 2000-11-20