### Table 1: Comparison of di erent discretization schemes.

"... In PAGE 9: ... The iterations were terminated when the 2-norm residual was reduced by 1010 orders of magnitude. We recorded in Table1 the number of iterations, the CPU time in seconds, and the maximum absolute discrete errors. All experiments were conducted on an SGI workstation using Fortran 77 programming language in double... In PAGE 9: ...Table 1: Comparison of di erent discretization schemes. The experimental results in Table1 support our analytic results in the previous two sections. The only exception is the iteration number for the second order scheme on the p2h grid with h = 1=32.... ..."

### Table 5 Discretization Scheme - Age Interval

"... In PAGE 15: ... The Mortality Dataset contains two continuous attributes: Age and Month. The discretization schemes of these attributes are shown in Table5 and Table 6 below. Each interval in these tables represents a consistent set of patterns (association rules).... In PAGE 15: ... A new interval is generated by the information- theoretic procedure, when there is a change in the rules explaining the target attribute. Thus, the death causes of infants (Age = 0) are different from children between the ages of one to three (see Table5 ). From looking at interval no.... ..."

### Table 7 The discretization scheme of the age dataset by CACC Class Interval Total

2007

"... In PAGE 9: ... The discrete result and the corresponding cacc of the age dataset are detailed in Table 6. Table7 is the final discrete result for the age dataset. We find CACC groups ages 15, 17, 21 in interval (10.... ..."

### Table 1. The order of convergence rate of the discretization scheme was computed as

2000

"... In PAGE 14: ...98 3.80 Table1 : Maximum errors and the estimated order of convergence rate for the fourth- order compact scheme. approximate solution of the rst order accuracy.... ..."

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### Table 3: Comparison of maximum absolute errors of the computed approximate solutions from di erent discretization schemes. Scheme

"... In PAGE 10: ... (13) and (16). However, the results in Table3 show that the solution computed from the fourth order compact di erence scheme is much more accurate than that computed from the second order di erence scheme. Table 2: Comparison of CPU time in seconds for multigrid method with di erent dis- cretization schemes and with line Gauss-Seidel relaxation.... In PAGE 11: ...CPU time) required for computing an approximate solution with a given accuracy. E.g., in the last row of Table3 , we nd that the computed solution with a maximum absolute error around 8:31 10?5 from the second order scheme uses Nx = 1024; Ny = 128. The data in the same location of Table 2 shows that the cost is 3:13 CPU seconds.... In PAGE 11: ... The data in the same location of Table 2 shows that the cost is 3:13 CPU seconds. For the fourth order compact di erence scheme, a more accurate approximate solution can be computed with Nx = 128; Ny = 64, see the third row of Table3 . The data in the same location of Table 2 shows that the computational cost of the fourth order compact di erence scheme is 0:19 CPU seconds.... In PAGE 11: ... The data in Table 2 show that the CPU seconds are more than doubled when either Nx or Ny is doubled. However, the results in Table3 show that increasing Ny does not always lead to reasonable increase in accuracy (small error) in the computed solution.... In PAGE 11: ...ead to reasonable increase in accuracy (small error) in the computed solution. E.g., the data in Table3 show that, for the fourth order compact di erence scheme, the least error 3:30 10?10 is achieved with Nx = 1024; Ny = 256 in 7:97 CPU seconds (Table 2). Use of equal mesh Nx = Ny = 1024 does not compute more accurate solution.... In PAGE 11: ... Use of equal mesh Nx = Ny = 1024 does not compute more accurate solution. The cost, however, is increased to 32:95 CPU seconds, see the data in the last row and last column of Table3 . This comparison demonstrates the advantage of using fourth order compact di erence scheme with unequal meshsizes.... ..."

### Table 2: Comparison of di erent discretization schemes for h = 1=32 with point Gauss- Seidel method.

"... In PAGE 8: ... We assume the computational grid is in rowwise natural ordering. In Table2 we compare the number of Gauss-Seidel iterations and the maximum absolute errors of the computed solution with respect to the exact physical solution, when di erent discretization schemes are used. This is done with a mesh size h = 1=32.... ..."

### Table 3: Comparison of di erent discretization schemes for h = =64 with point Gauss- Seidel method.

"... In PAGE 8: ... This is done with a mesh size h = 1=32. In Table3 , we repeat the comparisons, but with a ner mesh size h = 1=64. The numerical results in Tables 2 and 3 show that the computed solution from the fourth-order compact scheme is more accurate than those from the centered di erence and the upwind di erence schemes.... ..."

### Table 2 Quanta matrix. Frequency matrix for attribute F and discretization scheme D

### Table 1: Maximum errors and estimated accuracy order of di erent discretization schemes for Problem 1.

in High-Order Preconditioner and Re-Evaluation of Finite Difference Schemes for Convection-Diffusion

### Table 2: Maximum errors and estimated accuracy order of di erent discretization schemes for Problem 2.

in High-Order Preconditioner and Re-Evaluation of Finite Difference Schemes for Convection-Diffusion