### Table 3: Results of SDPA, SDPLIB with free var.

2005

"... In PAGE 9: ... In this way, we have a set of SDPs having free variables. Table3 and 4 show the results on SDPA applied to the standard form SDP (P2) and the converted SDP (P3) for solving these problems. SDPA applied to the SDP (P2) was not able to solve any of the problems except qap5 eq, qap6 eq and qap7 eq because of some numerical difficulties.... ..."

### Table 2: Performance and scalability of PDSDP when computing the elements of M, solving M using a Cholesky factorization, and solving the SDP

2003

"... In PAGE 8: ... For each problem, the first row shows the seconds required to compute (1) and assemble the matrix, given a dual matrix S in factored form. The second row in Table 1 indicates the seconds spent solving (1) using the conjugate gradient method, and the second row in Table2 indicates the time spent factoring the matrix M and solving (1) directly. The third row indicates the total seconds required by PDSDP to solve the problem.... In PAGE 11: ... The increased cost of computing each element of M reduced the percentage of time spent passing messages. Using the data in Table2 , the computation and assembly of M for control11, which has only 1526 constraints in standard form, had a parallel efficiency of 64% on 32 processors. This efficiency was much higher than the 28% achieved on theta4, which is a larger SDP.... ..."

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### Table 1 shows numerical results on the SDP relaxation of the BQIP with n = 100. ` denotes the number of iterations when the algorithm stopped because of a numerical di culty in Step 1-N or Step 1-BFGS; we regarded that the algorithm had gotten into a numerical di culty either when the number of iterations to determine a legitimate step length in Armijo apos;s rule exceeded m or when the number of iterations in Step 1-N or Step 1-BFGS to compute yk+1 from the initial point yk exceeded m. Also the following symbols are used.

2000

"... In PAGE 17: ...27e-4 2.90e-4 Table1 : SDP relaxation of box constrained QOPs with n = 100. then the dual of the SDP above turns out to be our standard form SDP (3).... In PAGE 18: ...From the numerical results in Table1 , we observe that all the variants could generate only low accuracy approximate optimal solutions; we need more sophisticated implementation to compute higher accuracy optimal solutions. Table 2 shows how the condition number of r2g(yk; k), the condition number of Lkr2g(yk; k)(Lk)T , where Lk(Lk)T denotes the Cholesky factorization of the quasi-Newton BFGS matrix Hk (see Section 3.... In PAGE 18: ... Table 2 shows how the condition number of r2g(yk; k), the condition number of Lkr2g(yk; k)(Lk)T , where Lk(Lk)T denotes the Cholesky factorization of the quasi-Newton BFGS matrix Hk (see Section 3.3), and # CG, the number of iterations in CG method in the predictor procedure changed along the sequence f(yk; k)g generated the BFGS + 2nd-order version applied to the SDP relaxation of the BQIP with n = 100 (the last column of Table1 ) . We see that the condition number of r2g(yk; k) had gotten worse rapidly as the iteration proceeds.... ..."

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### Table 2: Simulation results of SDP control policy (

2004

"... In PAGE 5: ... This simulation set-up allows us to study the performance of control algorithms under standard testing conditions. Through the continuous-time simulation, the performance of the control policy from SDP is compared with our prior work over different driving cycles as given in Table2 . The Rule-Based (DDP) refers to a rule-based control strategy trained based on the results of deterministic dynamic programming results [4].... ..."

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### Table 2. Performance measures stm lem fam f-sdp

"... In PAGE 6: ... The rst and second row show the total number of terms and unique terms obtained for the indexed documents, respectively, either for the source text and for the di erent con ated texts. Table2 shows performance measures as de ned in the standard trec eval program. The monolingual Spanish task in 2001 considered a set of 50 queries, but for one query any relevant document exists in the corpus, and so the performance measures are computed over 49 queries.... ..."

### Table 6: Numerical results on SDP relaxations of the graph partition problems. standard conversion completion

2003

"... In PAGE 19: ... Although (13) involves a dense data matrix E, we can obtain an equivalent SDP with sparse aggregate sparsity pattern applying an appropriate congruent transformation to it [8, section 6]. Table6 compares the three methods for the transformed problems. As k1 becomes large, the aggregate sparsity patterns remain sparse, though the extended sparsity patterns become dense for them.... ..."

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### Table 2 Factor Loadings of Cognitive Functioning (WAIS Abstract Reasoning) and Complexity of Work

2007

"... In PAGE 13: ... That is, between 1975 and 1993, each indicator is more persistent than one would expect from the combination of their dependence on the complexity of work and the persistence of overall work complexity across the 18 year period. Table2 displays standardized loadings of each indicator of cognitive functioning and work complexity on its latent variable. For convenience in reading, we have reversed the signs of loadings of the DOT variables relative to their original coding.... ..."

### Table 4: Numerical results on SDP relaxations of quadratic programs with box constraints. standard conversion completion

2003

"... In PAGE 18: ...minimize 12 0 @ 0 qT 0T q Q O 0 O O 1 A X subject to 0 @ 1 0T 0T 0 O O 0 O O 1 A X = 1; 0 @ 0 0T 0T 0 Eii O 0 O Eii 1 A X = 1 (i = 1; 2; ; n); X 2 S1+2n + 9 gt; gt; gt; gt; gt; gt; gt; gt; gt; gt; gt; = gt; gt; gt; gt; gt; gt; gt; gt; gt; gt; gt; ; : Here Eii 2 Sn denotes the matrix with (i; i)th element one and all others zeros. Table4 compares the three methods applied to this particular class of SDPs. denotes the average number of nonzeros per column of the matrix Q 2 Sn, and the vector q 2 Rn.... ..."

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### Table 5: Numerical results on SDP relaxations of the maximum cut problems. standard conversion completion

2003

"... In PAGE 19: ...Table5 compares the three methods for this problem. As k1 becomes large, the aggregate sparsity patterns remain sparse, though the extended sparsity patterns become dense for these SDPs.... ..."

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### Table 1: Comparison of SDP pruning, Diversity-based pruning, Kappa-pruning and original ensembles, by % error and (standard deviation)

2006

"... In PAGE 9: ... The greedy search picks classifier pairs from the ranked pair list until the pre-set size of the pruned ensemble is met. The performance of the three algorithms on the 24 data sets are listed in Table1 . Here, the size of the pruned ensemble is 25.... In PAGE 10: ... However, there is so far no strong evidence that such a meta-classifier is generally better than simple majority voting. Table1 shows that the performance of the SDP-based pruning is better than that of the other two algorithms for most of the data sets involved in the computational experiments. Also, although only a quarter of the classifiers are left, the error of the pruned ensemble by SDP-based pruning is statistically the same as that of the original ensemble.... ..."

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