### Table 14. Two-dimensional test problems.

1995

"... In PAGE 24: .... ALBERT, B. COCKBURN, D. FRENCH, AND T. PETERSON scheme: vi;j + H vi+1;j vi 1;j 2 x ; vi;j+1 vi;j 1 2 y !x vi+1;j 2vi;j + vi 1;j x2 !y vi;j+1 2vi;j + vi;j 1 y2 = fi;j; where we can take, for example, !x =sup (x;y)2 x 2 H1 @f @x(x; y); @f @y(x; y) ; !y =sup (x;y)2 y 2 H2 @f @x(x; y); @f @y(x; y) ; and Hi(p1;p2)=@H @pi (p1;p2)fori =1; 2. We apply this scheme to the two test problems in Table14 ; note that p =(p1;p2). In our numerical examples, in order to reduce the arti cial viscosity of the scheme, we replace f by the exact solution u in the formulae de ning !x and !y.... In PAGE 27: ...i usion. These subjects will also be considered in forthcoming papers. Acknowledgments. The authors would like to thank one of the referees, whose criticisms led to a complete revision of the paper, and also Timothy Barth for pointing out mistakes in Table14 and in the choice of the parameter ! for the computation of Tables 15 to 17 in an earlier version of the paper. References 1.... ..."

Cited by 12

### Table 3 Results for two-dimensional meshes.

1993

"... In PAGE 8: ... The top level separator for problems \airfoil 1 quot; and \venkat 2 quot; are shown in Figures 1 and 2; the vertices in the separator are marked by the symbol \ . quot; The results for two dimensional problems are summarized in Table3 . For = 1=3, the sizes of the subgraphs are balanced to within a factor of 2.... ..."

Cited by 11

### Table 3 Results for two-dimensional meshes.

1993

"... In PAGE 8: ... The top level separator for problems \airfoil 1 quot; and \venkat 2 quot; are shown in Figures 1 and 2; the vertices in the separator are marked by the symbol \ . quot; The results for two dimensional problems are summarized in Table3 . For = 1=3, the sizes of the subgraphs are balanced to within a factor of 2.... ..."

Cited by 11

### Table3 Results for two-dimensional meshes.

"... In PAGE 8: ... The top level separator for problems #5Cairfoil 1 quot; and #5Cvenkat 2 quot; are shown in Figures 1 and 2; the vertices in the separator are marked by the symbol #5C#0F. quot; The results for two dimensional problems are summarized in Table3 . For #0B =1=3, the sizes of the subgraphs are balanced to within a factor of 2.... ..."

### Table 1: A list of type-I two-dimensional EG- LDPC codes

2001

"... In PAGE 24: ...f decoding iterations to 50. Many codes have been simulated. Simulation results of all these codes show that the SPA decoding converges very fast. For example, consider the type-I two- dimensional (4095,3367) EG-LDPC code, the fifth code given in Table1 . Figure 8 shows the con- vergence of the SPA decoding for this code with C1 D1CPDC BP BDBCBC.... In PAGE 26: ... Example 3. For D1 BP BE and D7 BP BI, the type-I two-dimensional EG-LDPC code BV B4BDB5 BXBZ B4BEBN BIB5 is a (4095,3367) code with minimum distance 65, the fifth code given in Table1 . The parity check matrix of this code has row weight AQ BP BIBG and column weight AD BP BIBG, respectively.... In PAGE 26: ... Example 4. For D1 BP BE and D7 BP BJ, the type-I two-dimensional EG-LDPC code is a (16383, 14197) code with minimum distance 129, the sixth code in Table1 . The column and row weights of its parity check matrix are both 128.... In PAGE 29: ... Example 7. Again we consider the (4095,3367) type-I two-dimensional EG-LDPC code BV B4BDB5 BXBZ B4BEBN BIB5 given in Table1 . If we split each column of the parity check matrix H of this code into 16 columns and each row of H into 3 rows, we obtain a new parity check matrix C0 BC with column weight 4 and row weights 21 and 22.... ..."

Cited by 18

### Table 1: FEM results for the two{dimensional harmonic oscillator (eq.2) at di erent re nement levels and for polynomial degree p = 1; 2; 3. l

"... In PAGE 3: ... This leads to general matrix eigenvalue problems with dimension 5 for the initial grid up to dimensions 25000 { 46000 for the nal grids. For the rst eigenvalue 0 the results are given in Table1 . The nal matrix{dimension N is restricted by the core of the used workstation (Sun SPARC station 10).... In PAGE 4: ... Thus the asymptotic convergence of the adaptive FEM with linear elements is well described by i(Nl) := ~ i(Nl) ? i;exact = Ci Nl : (3) This can be used for an extrapolation, for instance if we use eigenvalues resulting from two re nement levels by the formula i;extr: = i(Nl) ? ( i(Nl?1) ? i(Nl)) Nl?1 Nl ? Nl?1 : (4) The extrapolated values are no longer upper bound, but are one digit more accurate and thus may be used (at least) for a very reliable error esti- mation. Proposing equation 4 to the last two levels of Table1 we get... ..."

### Table 7 LROLS selection procedure for the two-dimensional time series problem after k has converged (10 iterations)

2001

"... In PAGE 19: ... 9. The LROLS selection procedure, after k had converged (10 iterations), is listed in Table7 . Note that how many terms to include in the final model is a clear decision based only on the training set.... ..."

Cited by 9

### Table 6 Convergence factors (cf) for two-level implementations for the highly inde nite equation. No acceleration is used.

"... In PAGE 10: ...2. As a matter of fact, the results in Table6 coincide with those of Tables 5. When acceleration is used, the e ciency of ABOX for highly inde nite problems is shown.... ..."

### Table 4. Two-dimensional Coordinate Configuration.

"... In PAGE 7: ... The fIrSt is based on point scatter graphs, and the second simulates a terrain representation. Point Visualization The two-dimensional coordinates ( Table4 ) were input to Arc View in the fonD of event files (ESRI terminology) which made them readily available for visualization. The coordinate files were linked to ~e original keyword file (refer back to Table 1) through common identifiers, in straightforward GIS manner.... ..."

### Table 3. Two-dimensional contingency table

"... In PAGE 9: ... In our study we have two variables, real risk and predicted risk, that can assume only two discrete values, low and high, in a nominal scale. Thus the data can be represented by a two-dimensional contingency table, shown in Table3 , with one row for each level of the variable real risk and one column for each level of the variable predicted risk. The intersections of rows... ..."