### Table 5: Performance improvement by using the elimination forest guided approach.

1998

"... In PAGE 19: ... A comparison of the control strategies for exploiting 2D parallelism. In Table5 we assess the performance improvement by using the elimination forest guided approach against factor-ahead and basic approaches described in Section 4. Compared to the basic approach, the improvement... ..."

Cited by 13

### Table 5: Performance improvement by using the elimination forest guided approach.

1998

"... In PAGE 19: ... A comparison of the control strategies for exploiting 2D parallelism. In Table5 we assess the performance improvement by using the elimination forest guided approach against factor-ahead and basic approaches described in Section 4. Compared to the basic approach, the improvement... ..."

Cited by 13

### Table 5 Performance improvement by using the elimination forest guided approach.

2001

"... In PAGE 17: ...ig. 12. Performance improvement by using the supernodal GEMM. A comparison of the control strategies for exploiting 2D parallelism. In Table5 we assess the performance improvement by using the elimination forest guided approach against the factor-ahead and basic approaches described in Section 4. Compared to the basic approach, the improvement ratios vary from 16% to 41% and the average is 28%.... ..."

Cited by 4

### Table 1 Correspondence table relating definitions of Variables to bit positions for the local data flow computation of Fig. 5.

### Table 3: Black forest test.

2006

"... In PAGE 17: ...method (HMQ). For comparison we included in the table the grid errors for the same data obtained with the method (P) of [7], see Table3 in that paper. Since global methods based on ve of the above radial basis functions have been tested on ds3 in [12], we also included in Table 1 the corresponding grid errors reported there.... In PAGE 19: ... 16c]). Figures 5a and 5b (both related to the subregion indicated in Figure 3b) correspond to the tests reported in the rst and second rows of Table3 , respectively. Figure 5 has been obtained using the evaluations of the spline on the 1201 1201 grid (this is the same grid used to evaluate the errors in Table 3), while Figures 6a and 6b rely on the 421 421 evaluation grid in the subregion.... In PAGE 19: ... Figure 5 has been obtained using the evaluations of the spline on the 1201 1201 grid (this is the same grid used to evaluate the errors in Table 3), while Figures 6a and 6b rely on the 421 421 evaluation grid in the subregion. Table3 presents the parameters of each test, as well as the data errors max, mean and rms, average number of knots naver T and the computation CPU time t in seconds. As for the Franke function test, we take ny = nx, Mmax = 100 and do not provide P since there is no need in this tolerance in the case q = 0.... In PAGE 19: ...he case q = 0. Moreover, there have been no pure polynomial (i.e., constant) local approximations in these tests. For the ease of comparison, Table3 also includes the errors, the computation time and the values of nx and Mmin for the test with the method (P) reported in [7].... ..."

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### Table 2. Elimination lemmas

2004

"... In PAGE 3: ... Note that the de- pendency graph of the constructions must be cycle free. To eliminate a point from the goal we need to apply one of the elimination lem- mas shown on Table2 on page 5. This table can be read as follows: To eliminate a point Y , choose the line corresponding to the way Y has been constructed, and apply the formula given in the column corresponding to the geometric quantity in which Y is used.... In PAGE 4: ... We rst translate the goal (A0B0 k AB) into its equivalent using the signed area: SA0B0A = SA0B0B Then we eliminate compound points from the goal starting by the last point in the order of their construction. The geometric quantities containing an oc- currence of B0 are SA0B0B and SA0B0A, B0 has been constructed using the rst construction on Table2 with = 1 2: SA0B0A = SAA0B0 = 1 2SAA0A + 1 2SAA0C = 1 2SAA0C and SA0B0B = SBA0B0 = 1 2SBA0A + 1 2SBA0C The new goal is SAA0C = SBA0A + SBA0C Now we eliminate A0 using: SCAA0 = 1 2SCAB + 1 2SCAC = 1 2SCAB SABA0 = 1 2SABB + 1 2SABC = 1... In PAGE 11: ... This tactic (called eliminate_all) rst searches the con- text for a point which is not used to build another point (a leaf in the dependency graph). Then for each occurrence of the point in the goal, it applies the right lemma from Table2 by nding in the context how the point has been constructed and which geometric quantity it appears in. Finally it removes the hypotheses stating how the point has been constructed from the context.... In PAGE 12: ...this classical reasoning step. As noted before, the elimination lemmas given in Table2 on page 5, do eliminate an occurrence of a point Y only if Y appears only one time in the geometric quantity (A,B,C and D must be di erent from Y ). If Y appears twice in S, this is not a problem because then the geometric quantity is zero, and so already eliminated by the simpli cation phase.... ..."

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### Table 1. Change in forest cover by forest type from 1993-2000

2005

"... In PAGE 6: ...iv Tables Page Table1 .... In PAGE 11: ... The highest rates of deforestation in the sample are found in the states of Veracruz and Yucatan, followed by Colima and Puebla, with moderately high rates throughout the Northern Sierra region and Quintana Roo. This corresponds with the observation from Table1 that tropical forests are subject to higher rates of loss than temperate ones. Note that there were several... ..."

### Table IV. Domains of the variables for the proper forest constraint corresponding to parts (A) and (B) of Figure 15.

### Table 1: The checkpointing overhead for the phases of radix. n is the number of keys to be sorted, p is in the number of nodes, and r is the size of radix. 7.2 LU Dense LU factorization is the process of converting a dense matrix A into two matrices L, U that are lower- and upper-triangular, respectively, and whose product equals A. LU factorization works like Gaus- sian elimination, eliminating one variable at a time by subtracting rows of the matrix by scalar multiples of other rows. In order to exploit temporal locality, most implementations of the LU factorization use a technique called blocking in which the N-by-N matrix 10

"... In PAGE 10: ... At the end of the permutation phase, the amount of shared data written to checkpoint record by node 0 is n=p2 since node 0 writes n=p keys and the probability each key is written to the rst p positions of the output array is 1=p. The checkpointing overhead at the end of each phase of radix is summarized in Table1 . Note that in the permutation phase, the amount of data check- pointed by our scheme is smaller than the amount of... ..."

### Table 4: Experimental Results: Unreachable Code Elimination

1998

"... In PAGE 8: ... This analysis also makes use of context information as a basic block that follows a function call will be marked reachable if the corresponding call site is reachable, rather than the function that is called as the function could already be reachable due to a call from another call site. The amount of unreachable code detected in our benchmarks is shown in Table4 . These numbers do not include no-ops inserted into reachable basic blocks for alignment and instruction scheduling purposes.... ..."

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