### Table 0:1: Algorithms

"... In PAGE 2: ... The last column contains further references. Table0 :2: Matrices Matrix A 2 Cn n Prep(A) Comp(A; b) References Fourier matrix | (n) Well known and its inverse Factor circulant (n) + O(n) 2 (n) + O(n) Well known Toeplitz matrix 2 (n) 4 (n) + O(n) Well known Vandermonde matrix | quot;(n) Well known Inverse of | (n) Well known Vandermonde matrix Transpose of (n) + quot;(n) + (n)+ (n) + 2 (n) + O(n) [11] Vandermonde matrix +2n log n + O(n) (see also [5]) Transpose of inverse (n) + quot;(n) + (n)+ quot;(n) + 2 (n) + O(n) [11] Vandermonde matrix 1 +2n log n + O(n) (see also [5]) Cauchy matrix (n) + 2 quot;(n) + O(n) (n) + quot;(n) + O(n) [8], [11] 1Algorithms from [11] for transpose to Vandermonde matrix and for transpose to inverse Vandermonde matrix have the same preprocessing stage.... ..."

### Table 3. Performance Estimates for a Scalable Switch ~N for 1 3 2, 2 3 2, and 4

"... In PAGE 11: ... 17. Table3 lists the performance val- ues required of a 2 3 2 BCGH switch for large switches ~N $ 1024! and the best experimental re- sults obtained to date. Note that the increased cross talk of approximately 3 dB for the experimental 4 3 4 Stretch switch versus that of the 2 3 2 switch is consistent with the predicted values from Table 2 ~ASyPC!.... ..."

### TABLE I11 SYSTEM RELIABILITIES: R, IS THE RELIABILITY OF A DR-BASED NONPARTITIONABLE SYSTEM OF SIZE N + 1. R, IS THE RELIABILITY OF A DR-BASED OR RDR-BASED PARTITIONABLE SYSTEM OF SIZE N + Q

### TABLE I1 RELIABILITIES OF NONPARTITIONABLE SYSTEMS AT DIFFERENT VALUES OF S. WHEN S 2 1, A DR NETWORK OF SIZE N + s IS USED

### Table 4. Submodel is correct: n = 10 ; b0 = 1 .

"... In PAGE 19: ...cf M2 corr and c M2 are exhibiting only little bias for estimating Ave( e Ln+1) and Ave(Ln+1) , respectively: even though the structural parameters are estimated and exact unbiasedness is not true anymore. Tables 1 - 3 about here In Table4 we show one situation where the Submodel is correct. We only report the case with individual sample size n = 10 ; the cases with n = 5 and n = 20 gave similar results.... In PAGE 19: ... But we would expect a bigger di erence between Ave( e Ln+1) and Ave(Ln+1) when the di erence in dimensionality between the Full Model and the Submodel would be much bigger than one, because of the e ect of estimated structural parameters. Table4 about here Summarizing the whole simulation study: in the case where the underlying model is unknown (which is always true in practice), the average loss Ave(L n+1) in the model chosen by our criterion is very close to the optimal loss, which is most often, but not always, achieved with the correct unknown model. Conclusions We have developed a data{driven rule for choosing between a location and a linear trend credibility model.... ..."

### Table 1. Problem Statistics of 51 0/1 MIPLIB Problems

1995

"... In PAGE 4: ... In addition to applying standard linear programming (LP) reductions, also valid for integer programs, CPLEX applies \coe cient reduction quot; and \bound strengthening, quot; see [19]. Statis- tics for the problems solved and the preprocessed versions are given in Table1 . We remark that, without preprocessing, our code could not solve the model mod011 from MIPLIB, and its performance was seriously a ected in a number of other cases.... In PAGE 12: ...ll processors after printing the solution. We de ne the speedup for n processors to be the ratio T1=Tn. (See the later discussion of the alternative measure T1?Tstartup Tn?Tstartup .) Table1 shows problem statistics. Here, Name, Original Rows, Cols, and 0/1 var denote, respectively, the name of the test instance, the initial number of rows, the number of columns, and the number of 0/1 variables in the constraint matrix.... ..."

Cited by 12

### Table 1. Problem Statistics of 51 0/1 MIPLIB Problems

"... In PAGE 3: ... In addition to applying standard linear programming (LP) reductions, also valid for integer programs, CPLEX applies \coe cient reduction quot; and \bound strengthening, quot; see [19]. Statis- tics for the problems solved and the preprocessed versions are given in Table1 . We remark that, without preprocessing, our code could not solve the model mod011 from MIPLIB, and its performance was seriously a ected in a number of other cases.... In PAGE 9: ...ll processors after printing the solution. We de ne the speedup for n processors to be the ratio T1=Tn. (See the later discussion of the alternative measure T1?Tstartup Tn?Tstartup .) Table1 shows problem statistics. Here, Name, Original Rows, Cols, and 0/1 var denote, respectively, the name of the test instance, the initial number of rows, the number of columns, and the number of 0/1 variables in the constraint matrix.... ..."

### Table III. We include two run-length symbols 0(+1) and 0(?1). The trellis structure for this example is shown in Figure 3. Including run-length symbols can result in better performance for small bit-rates R. Note that when run coding is employed, the resulting trellis has the interesting feature of branches that span multiple columns (e.g., see the branches that go from state (0,0) to state (2,3)). Note also that the trellis of Figure 3 has two \extra quot; branches (labeled +1 and -1) going from node (1,1) to node (2,4). These branches allow the encoder the possibility of encoding sequences without using run coding (i.e., 0, 1 and 0, -1 can be encoded as is, or as their run-coded versions 0(+1) and 0(-1) ). For a properly designed run/Hu man code, these \extra quot; branches provide no performance bene t (or degradation). They are included only to ease the description and programming of the algorithm.

### Table 4. Points : Chebyshev zeros in (0,1), RHS : 1.

1997

"... In PAGE 11: ...able 4. Points : Chebyshev zeros in (0,1), RHS : 1. Random Monotonic Leja ordering ordering ordering GJECP Traub B-P Parker B-P Parker B-P Parker n 2(V ) kak2 ed es es es es es es es es 5 3e+03 2e+03 4e-16 6e-06 2e-05 2e-07 2e-07 2e-07 2e-07 3e-07 2e-07 10 2e+08 8e+07 2e-15 3e+00 9e-01 7e-08 2e-07 4e-07 3e-07 3e-07 2e-07 20 6e+17 4e+17 1e-15 1e+00 1e+00 4e-06 9e-07 9e-07 1e-06 4e-06 1e-06 30 6e+18 3e+27 5e-14 1e+00 1e+00 2e-04 7e-07 7e-07 7e-07 2e-05 7e-07 40 4e+18 3e+37 4e-12 1e+00 1e+00 5e-04 1e-06 2e-06 1e-06 5e-03 1e-06 45 7e+18 3e+42 4e-11 1e+00 1e+00 Inf Inf Inf Inf Inf Inf This is the most favorable for the Bjorck-Pereyra algorithm case of positive, monotonically ordered points xk and sign-interchanging right-hand side, and as shown in [Hig87], the Bjorck-Pereyra algorithm is guaranteed to compute in this case a remarkably accurate solution ^ a : j^ a ? aj 5nu jaj + O(u2): (6.1) Table4 demonstrates that the accuracy of the Bjorck-Pereyra algorithm, combined with mono- tonic ordering, is indeed compatible with the remarkable bound in (6.1).... ..."

Cited by 2

### Table 6. Classi cation of (0; 1) matrices of order n 7

"... In PAGE 9: ...9 exist a SNF class, consisting of more than one -class, is 5. In Table6 the complete list of -representatives in An is given for n 7. The representatives are given by hexadecimaly coded rows.... In PAGE 14: ...MIODRAG ZIVKOVI C Table6 . Continued n SNF det -size -size the -representative 16 1 1 1 1 1 2 2 442 17642 1 2 4 18 28 30 17 1 1 1 1 1 3 3 128 4079 1 2 C 14 24 38 18 1 1 1 1 1 4 4 52 1685 1 6 A 12 22 3C 19 1 1 1 1 1 5 5 17 427 1 6 A 1C 2C 32 1 2 3 5 9 11 21 3E 20 1 1 1 1 2 2 4 17 473 1 6 18 2A 2C 32 21 1 1 1 1 1 6 6 9 263 3 5 9 16 2E 31 22 1 1 1 1 1 7 7 1 6 3 5 9 1E 2E 31 2 48 3 5 E 18 29 36 23 1 1 1 1 1 8 8 1 6 3 5 E 19 29 36 1 21 3 C 15 1A 26 39 24 1 1 1 1 2 4 8 1 12 3 C 15 1A 26 29 25 1 1 1 1 1 9 9 1 7 3 D 15 1A 26 39 26 1 1 1 2 2 2 8 1 2 7 19 1E 2A 2D 33 7 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 16 49 0 0 0 0 0 0 1 3 1 1 0 0 0 0 0 0 170 1428 0 0 0 0 0 1 2 4 1 1 1 0 0 0 0 0 1908 31994 0 0 0 0 1 2 4 5 1 1 2 0 0 0 0 0 34 246 0 0 0 0 3 5 6 6 1 1 1 1 0 0 0 0 17596 501563 0 0 0 1 2 4 8 7 1 1 1 2 0 0 0 0 694 13645 0 0 0 1 6 A C 8 1 1 1 3 0 0 0 0 30 400 0 0 0 3 5 9 E 9 1 1 1 1 1 0 0 0 105808 4358421 0 0 1 2 4 8 10 10 1 1 1 1 2 0 0 0 9295 316904 0 0 1 2 C 14 18 11 1 1 1 1 3 0 0 0 853 22902 0 0 1 6 A 12 1C 12 1 1 1 1 4 0 0 0 9 92 0 0 3 5 9 11 1E 159 3622 0 0 3 5 A 16 19 13 1 1 1 1 5 0 0 0 23 413 0 0 3 5 E 16 19 14 1 1 1 2 2 0 0 0 58 1032 0 0 3 C 15 16 19 15 1 1 1 1 1 1 0 0 261882 13834240 0 1 2 4 8 10 20 16 1 1 1 1 1 2 0 0 53874 2624469 0 1 2 4 18 28 30 17 1 1 1 1 1 3 0 0 8633 376699 0 1 2 C 14 24 38 18 1 1 1 1 1 4 0 0 3024 123510 0 1 6 A 12 22 3C 19 1 1 1 1 1 5 0 0 631 23474 0 1 6 A 1C 2C 32 2 15 0 3 5 9 11 21 3E 20 1 1 1 1 2 2 0 0 927 37489 0 1 6 18 2A 2C 32 21 1 1 1 1 1 6 0 0 361 13823 0 3 5 9 16 2E 31 22 1 1 1 1 1 7 0 0 6 93 0 3 5 9 1E 2E 31 58 2040 0 3 5 E 18 29 36 23 1 1 1 1 1 8 0 0 6 113 0 3 5 E 19 29 36 19 415 0 3 C 15 1A 26 39 24 1 1 1 1 2 4 0 0 27 893 0 3 C 15 1A 26 29 25 1 1 1 1 1 9 0 0 7 189 0 3 D 15 1A 26 39 26 1 1 1 2 2 2 0 0 2 25 0 7 19 1E 2A 2D 33 1 2 0 F 33 3C 55 5A 66 27 1 1 1 1 1 1 1 1 91764 5593528 1 2 4 8 10 20 40 28 1 1 1 1 1 1 2 2 58179 3493129 1 2 4 8 30 50... In PAGE 15: ...15 Table6 . Continued n SNF det -size -size the -representative 29 1 1 1 1 1 1 3 3 17707 1020752 1 2 4 18 28 48 70 30 1 1 1 1 1 1 4 4 10189 581948 1 2 C 14 24 44 78 31 1 1 1 1 1 1 5 5 3169 172714 1 2 C 14 38 58 64 32 1 1 1 1 1 2 2 4 3220 184475 1 2 C 30 54 58 64 33 1 1 1 1 1 1 6 6 3319 185686 1 6 A 12 2C 5C 62 1 2 3 5 9 11 21 41 7E 34 1 1 1 1 1 1 7 7 749 39068 1 6 A 12 3C 5C 62 35 1 1 1 1 1 1 8 8 645 32490 1 6 A 1C 32 52 6C 36 1 1 1 1 1 2 4 8 317 15119 1 6 18 2A 34 4C 52 37 1 1 1 1 1 1 9 9 252 12603 1 6 1A 2A 34 4C 72 1 6 3 5 9 11 3E 5E 61 38 1 1 1 1 2 2 2 8 29 750 1 E 32 3C 54 5A 66 39 1 1 1 1 1 1 10 10 1 3 3 5 9 1E 2E 4E 71 198 10091 3 5 9 1E 30 51 6E 40 1 1 1 1 1 1 11 11 1 11 3 5 9 1E 31 51 6E 54 2587 3 5 E 16 38 59 66 41 1 1 1 1 1 1 12 12 1 7 3 5 E 16 39 59 66 69 3235 3 5 E 19 32 56 69 1 21 3 5 19 2E 36 4E 61 42 1 1 1 1 1 1 13 13 1 9 3 5 E 19 36 56 69 15 658 3 5 18 29 36 4E 71 1 19 3 5 19 29 3E 4E 71 43 1 1 1 1 1 3 3 9 37 1358 3 5 18 28 49 4E 71 44 1 1 1 1 1 2 6 12 1 21 3 5 19 29 36 4E 51 26 962 3 5 19 2A 36 4E 61 1 14 3 D 31 3E 55 5A 66 45 1 1 1 1 1 1 14 14 1 19 3 5 19 29 36 4E 71 9 496 3 C 15 26 39 5A 65 2 100 3 D 15 26 38 5A 61 46 1 1 1 1 1 1 16 16 1 30 3 C 15 36 39 5A 65 3 62 3 D 16 2A 31 58 65 1 21 3 D 16 2A 35 59 66 47 1 1 1 1 2 2 4 16 2 10 3 C 30 55 5A 66 69 48 1 1 1 1 1 2 8 16 5 89 3 C 31 55 5A 66 69 1 13 3 D 31 55 5A 66 69 49 1 1 1 1 1 4 4 16 1 6 3 C 35 3A 55 66 69 1 7 3 D 16 2A 31 59 66 50 1 1 1 1 1 1 15 15 3 59 3 D 15 26 38 5E 61 1 28 3 D 15 26 39 5A 65 2 128 3 D 16 2A 35 58 66 51 1 1 1 1 1 1 17 17 1 19 3 D 16 2E 39 5A 65 1 8 7 19 2A 35 4C 69 72 52 1 1 1 1 1 3 6 18 1 2 3 1D 2D 36 3A 4E 71 1 8 7 19 2A 34 4D 56 63 53 1 1 1 1 2 2 6 24 1 5 7 19 2A 34 4C 52 61 54 1 1 1 1 1 2 10 20 1 10 7 19 2A 34 4C 52 63 55 1 1 1 1 1 1 18 18 1 24 7 19 2A 34 4C 53 65 56 1 1 1 2 2 2 4 32 1 1 F 33 3C 55 5A 66... ..."