### Table 4. As our last example we choose the M-matrix

"... In PAGE 24: ...23 Table4 . Residuals for the Class of Diagonally Dominant Matrices.... In PAGE 25: ... For the second and third class of test problems the condition (69) always holds. For these cases, the results in Table4 and 6 con rm that Algorithm 1 can compute a solution with a residual whose norm is on the same order as the norm of the residual from Gaussian elimination. 10.... ..."

### Table 1 M Matrix for Hierarchical Factor Data

"... In PAGE 8: ...08) between variables associated with the same group factor and low (weak interaction H11005 .02) between variables of different group factors (see Table1 ). To demonstrate this, we simulated data for four group factors, each associated with four variables xi.... ..."

### Table I. Timings using floating-point double precision, fi lib in- terval arithmetic and MPFI arbitrary precision interval arithmetic on Gaussian elimination on a M-matrix of dimension 300.

2002

Cited by 16

### Table 1: M and N Matrices for Various Stationary Iterative Solvers Solver M Matrix N Matrix

"... In PAGE 9: ...Stationary Multiplicative Iterative Solvers At the core of the AMG smoothers S(Al; ul; bl) are stationary multiplicative solvers of the form u(k+1) = Mlu(k) + Nlb ; (11) where Ml and Nl are derived from Al via matrix splitting. Table1 illustrates the structure of the M and N matrices for the Jacobi, Gauss-Seidel, and SOR iterative methods. D is the diagonal of A and ?L and ?U are the upper and lower triangular parts of A, respectively [13].... In PAGE 22: ... As in the 2D example, the AMG runtimes include the time required to setup of the coarse levels and interpolation operators. Table1 0: 3D Pillar Analysis Runtimes - Single Workstation Mesh PCG Runtime AMG Runtime AMG Runtime (swap) (minutes) (minutes) (minutes) Uniform Elements 32 47 1,366 Non-uniform Elements 125 98 3,038 As with the 2D foundation example, the runtimes indicate that PCG is better suited for problems involving uniform meshes and AMG is better suited to meshes involving poorly scaled elements. In addition, some swap delays did occur during the generation of the coarse levels for the non-uniform mesh on the single workstation run of the AMG algorithm.... In PAGE 26: ...Table1 1: Numerical Results for 3D Pillar Analysis - Uniform Mesh Displacement Stress (PCG) Stress (AMG) (kN m2 ) (kN m2 ) 0.050 -25.... In PAGE 26: ...33 -59.96 Table1 2: Distributed Algorithms Speedups - No Swapping Uniform Mesh Algorithm Workstations 2 3 4 5 Distributed Levels 0.64 0.... In PAGE 27: ...Table1 3: 3D Pillar Analysis Runtimes - Distributed Algorithms/Uniform Mesh Algorithm Workstations 2 3 4 5 Runtime Runtime Runtime Runtime (minutes) (minutes) (minutes) (minutes) Distributed Levels 73 72 71 N/A Distributed Levels (parallel) 62 63 62 N/A Distributed A1 91 94 104 120 Table 14: 3D Pillar Analysis Runtimes - Distributed Algorithms/Non-uniform Mesh Algorithm Workstations 2 3 4 5 Runtime Runtime Runtime Runtime (minutes) (minutes) (minutes) (minutes) Distributed Levels 92 93 93 N/A Distributed Levels (parallel) 79 78 80 N/A Distributed A1 118 133 150 155 [5] H. Regler and U.... In PAGE 27: ...Algorithm Workstations 2 3 4 5 Runtime Runtime Runtime Runtime (minutes) (minutes) (minutes) (minutes) Distributed Levels 73 72 71 N/A Distributed Levels (parallel) 62 63 62 N/A Distributed A1 91 94 104 120 Table1 4: 3D Pillar Analysis Runtimes - Distributed Algorithms/Non-uniform Mesh Algorithm Workstations 2 3 4 5 Runtime Runtime Runtime Runtime (minutes) (minutes) (minutes) (minutes) Distributed Levels 92 93 93 N/A Distributed Levels (parallel) 79 78 80 N/A Distributed A1 118 133 150 155 [5] H. Regler and U.... In PAGE 27: ....J. Evans, editor, Sparsity and Its Applications, Cambridge, MA, 1984. Cambridge University Press. Table1 5: Distributed Algorithms Speedups - Swapping Uniform Mesh Algorithm Workstations 2 3 4 5 Distributed Levels 18.71 18.... ..."

### Table 4: Compar. eval. of the (E)dit and (M)atrix methods for types 0 , 1 and (No) paraphrases.

2007

"... In PAGE 40: ... Labeler 1 shows an accuracy of 74% on the algorithm and 72% on the baseline; Labeler 2 has an accuracy of 73% on the algorithm and 69% on the baseline. Evaluation Labeler 1 Labeler 2 Algorithm Accuracy 74% 73% Baseline Accuracy 72% 69% Top3 79% 79% Top5 81% 80% Table4 : Results for Test Set (n=275 terms) 4.3 Results for Ambiguous Terms This section shows the results for the terms from the training set and the test set that required dis- ambiguation.... In PAGE 49: ... Table 4 presents a complete list of subjects of the active voice of the verb mitto (to send) as attested in our treebank. angelus angel Caesar Caesar deus God diabolus devil Remi Gallic tribe serpens serpent ficus fig tree Table4 : Subjects of active mitto in the Latin Depen- dency Treebank 1.3.... In PAGE 88: ...7133 Table 3: Mean Reciprocal Rank and Success@10 for all topic sets on the web site objects. Topic set System ranking Raw A follows B followsequal C follows F follows E follows D follows I follows H follows G Union C follows B follows A follows F follows E follows D follows I follows H follows G Intersection C follows B follows A follows F follows E follows D follows I follows H follows G KI-topics C follows B follows F follows E follows A follows I follows D follows H follows G Table4 : Systems rankings of the 4 topic sets.... In PAGE 89: ...eciprocal rank (i.e., 1 over the rank at which the first relevant document is found). The rankings over the four different topic sets are given in Table4 (based on the labeling introduced in Table 2). The results show that ranking based on the Raw Topic set deviates slightly from ranking based on the Union and Intersection topic sets.... In PAGE 97: ...0388 P@10 = 0.1000 Table4 : Results for AKW1 field search. (RUNmt+t run provides the best results in all cases.... ..."

### TABLE III Diagnostic specificity of class prediction based on ANN training with standardized expression for selected genes. k-means

### Table 5: CPU times (in seconds) and matrix-vector products for the TOLOSA matrix of order 1000 ( denotes that code did not converge within 4000m matrix-vector products)

1996

Cited by 30

### Table 5: CPU times (in seconds) and matrix-vector products for the TOLOSA matrix of order 1000 ( denotes that code did not converge within 4000m matrix-vector products)

1996

Cited by 30

### Table 13: Computation time of major parts of SDPA applied to control and system theory problems.

1997

"... In PAGE 21: ...0 - 35 - 9.91e-06 - Table13 gives the CPU time required in major parts of SDPA applied to the two largest cases shown in Table 12. Compared with the previous three problems (see Tables 8 and 11), part (II) consisting of the LDLT factorization of the m m matrix B now constitutes a much larger percentage of the computation time.... ..."

Cited by 25

### Table 12: Numerical results on control and system theory problems

1997

"... In PAGE 21: ... This phenomenon occurred because the primal feasible region is narrow, so that both algorithms need much time to reach the feasible region. Particularly, SDPT3 stopped with the message \lack of progress in corrector quot; and \lack of progress in predictor quot; in the cases of k = ` = 20 and 25, respectively, before it would attain a relative gap less than 10?5 (see the numbers with ? in Table12 ). In most of the cases, however, we observed that once SDPA and SDPT3 moved into the feasible region, they attained an approximate optimal solution with a given accuracy in a few steps.... In PAGE 21: ...Table 13 gives the CPU time required in major parts of SDPA applied to the two largest cases shown in Table12 . Compared with the previous three problems (see Tables 8 and 11), part (II) consisting of the LDLT factorization of the m m matrix B now constitutes a much larger percentage of the computation time.... ..."

Cited by 25