### TABLE I Asymptotic and finite convergence properties of the

1994

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### Table 2 can be neglected compared with the construction of the H-matrix approximant. Iterating without any preconditioner does not converge at all. Note that preconditioners which guarantee an asymptotic boundedness of the condition number with respect to n based on the mapping properties of the operator (see [19]) will not be enough in order to obtain a reasonable convergence behaviour. The bad condition number is caused by the geometry and not by n.

"... In PAGE 16: ...1 96 8.9s Table2 : Preconditioned MinRes for the domain from Fig. 2.... ..."

### Table 1: Results for simulation experiment 1.

1999

"... In PAGE 6: ... The purpose of this experiment was to assess asymptotic convergence properties, in particular estimator er- ror and variance. As can be seen from Table1 , the reducing beta schedule of i = 1=i was superior to xed beta and ccBeta in terms of both total square error (TSE) and estimator variance for this experiment. As we would expect, variance (normalised to standard de- viation in the tabled results) increased directly with the magnitude of beta for the xed beta series.... ..."

Cited by 1

### Table 1: Results for simulation experiment1.

"... In PAGE 10: ... The purpose of this experimentwas to assess asymptotic convergence properties, in particular estimator error and variance. As can be seen from Table1 , the reducing beta schedule of i = 1=i was superior to xed beta and ccBeta in terms of both total square error (TSE) and estimator variance for this experiment. As we would expect, variance... ..."

### Table 1: Results for simulation experiment 1.

"... In PAGE 10: ... The purpose of this experiment was to assess asymptotic convergence properties, in particular estimator error and variance. As can be seen from Table1 , the reducing beta schedule of i = 1=i was superior to xed beta and ccBeta in terms of both total square error (TSE) and estimator variance for this experiment. As we would expect, variance... ..."

### Table 1: Results for simulation experiment 1. Once an autocorrelation coe cient is derived, i is set as follows:

"... In PAGE 5: ... The purpose of this experiment was to assess asymptotic convergence properties, in particular estimator error and variance. As can be seen from Table1 , the reducing beta schedule of i = 1=i was superior to xed beta and ccBeta in terms of both total square error (TSE) and estimator variance for this experiment. As we would expect, variance (normalised to standard deviation in the tabled results) increased directly with the magni- tude of beta for the xed beta series.... ..."

### Table 1 Asymptotic properties.

1998

"... In PAGE 15: ... Such a simple example su ces to demonstrate the poorness of the asymptotic approximation. The results are given in Table1 , and it is seen that even for very large sample sizes the approximation is not good. In fact a rectangular weight function on [?1; 1] gave somewhat better results, the empirical sizes for ^ L2(M1), ^ L2(M0 1) and ^ L2(M00 1 ) being 0.... In PAGE 15: ... As in Hjellvik and Tj stheim (1995), a better nite sample t can be obtained by using a gamma distribution (or 2 distribution), but the problem of a very poor approximation to the location and scale parameters persists (cf. Table1 ). Better approximation in a spesial case using a xed experimental design have been reported by Poggi and Portier (1995).... In PAGE 17: ...1) with a = 0:5. By comparison to Table1 it is seen that the results obtained represent a vast improvement over those which could be achieved using asymptotic theory, where the size would be drastically underestimated for ^ L2(M1) and overestimated for ^ L2(M0 1) and ^ L2(M00 1 ). It is seen that ^ L0(M1) collapses when h 1:0, the other statistics seem to be quite independent of h.... In PAGE 37: ... The bandwidth is cross-validated according to Table 3, and the upper limit of the estimated order of the autoregressive t is ^ p = n=10. Table captions Table1 : The ratio between the asymptotic values given by Theorem 3.2 and simulated values for the mean and standard deviation of ^ L2(M1), ^ L2(M0 1) and ^ L2(M00 1 ), and the empirical sizes for these statistics when they have been centered by the asymptotic mean and scaled by the asymptotic standard deviation of Theorem 3.... ..."

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### Table 2. Asymptotic numerical convergence rate j and theoretical convergence rate j (3.17) for some of the leftmost eigenvalues of the five sample problems.

"... In PAGE 9: ...17) is well approximated by j. Table2 makes a comparison of j and j for some j values of the five sample problems. We notice that the theoretical value j and the numerical one j are indeed very close also for j lt; 2.... ..."

### TABLE I ASYMPTOTIC BOUNDS ON THE CONVERGENCE TIME.

2005

Cited by 5

### Table 1 Asymptotic multigrid convergence factors

1997

Cited by 3