### Table 1: Perturbation bounds.

1997

"... In PAGE 9: ... The second column gives the actual value of k P k, and the other columns give error bounds computed from Theorem 1, (21) and (22), respectively. From Table1 we can make some interesting observations which also depict the general behaviour. Our bound is better for subspaces which correspond to tiny (clustered) eigenvalues which have large relative gaps, and small absolute gaps (T2, T23, T234, T2345, and T5).... ..."

Cited by 2

### Table 1: Perturbation bounds.

1999

"... In PAGE 10: ... Since relative gaps are moderate in all cases, from Remark 2 we conclude that all of QT were computed to almost full accuracy. The same holds for all of e QT , thus the computed values of k P k which are displayed in Table1 are almost equal to the exact ones. From Table 1 we can make some interesting observations which also depict the general behavior.... In PAGE 10: ... The same holds for all of e QT , thus the computed values of k P k which are displayed in Table 1 are almost equal to the exact ones. From Table1 we can make some interesting observations which also depict the general behavior. The bound of Theorem 1 is usually sharper than the classical bounds (2) and (3) for subspaces which correspond to tiny (clustered)... ..."

Cited by 2

### Table 1: Perturbation bounds.

1999

"... In PAGE 10: ...From Table1 we can make some interesting observations which also de- pict the general behavior. Our bound is usually sharper for subspaces which correspond to tiny (clustered) eigenvalues which have large relative gaps, and small absolute gaps (T2, T23, T234, T2345, and T5).... ..."

Cited by 2

### Table 5: Perturbation bounds of the indefinite polar factorization.

2005

"... In PAGE 21: ... We shifted all these matrices so that JAT epsilon1 JAepsilon1 has all its eigenvalues in the open right half-plane. The results are displayed in Table5 . We see that our perturbation bounds follow closely the computed values which confirms that in this case the bounds obtained by Theorem 5.... ..."

### Table 3: Comparison on the same problems with perturbed bounds

### Table 5: CPU times for perturbation off the bounds

1994

Cited by 5

### Table 6: Perturbation bounds of the IPF using bounds of the condition number cH and cS.

2005

"... In PAGE 21: ...ase the bounds obtained by Theorem 5.4 are sharp. We denote by cH and cS the bounds of the condition number of the hyperbolic and symmetric factors given by (66)-(67). Table6 shows the first order perturbation bounds obtained by using cH and cS. The bounds obtained by using csand cH in the first 4 rows in Table in 6 are accurate.... ..."

### Table 6.1 gives the corresponding relative gaps from (6.37), the exact perturbations and the bound (6.38).

### Table 2: Bounds for k = 10 (perturbed reward r)

2004

### Table 1: Eigenvector perturbations

2000

"... In PAGE 11: ... Let sin i = sin (xi; e xi), where xi is the eigenvec- tor of i. Table1 gives the corresponding relative gaps, the exact perturbations and the bounds computed by Corollary 2.... ..."

Cited by 5