### Table 1 Low-rank criteria when (I + G)s = t is solved in parallel.

1996

"... In PAGE 13: ... If n gt; p3, which is a reasonable assumption for most parallel architectures and practical problem sizes, only the second values in the formulas (16,18) with the min operator apply. Table1 summarizes the order estimates for parallel factorization of and solu- tion with I + G, and Table 2 presents results for the sequential case. Suppose that A is the matrix for a discretized PDE on a cubic domain divided into cubic subdomains, and QC (or QL + QR) is composed of the original o - diagonal blocks of A.... ..."

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### Table 1 Low-rank criteria (in the case of parallel solving of (I + G)s = t).

1995

"... In PAGE 8: ... Restrictions on m that are necessary to satisfy criterion (b) can be derived from the estimates of tG given earlier in this section. These results for parallel factoring of I + G and parallel (I + G)-solve are sum- marized in Table1 . Table 2 presents analogously obtained results for sequential LU- factoring and (I + G)-solve.... ..."

Cited by 1

### Table 1 Low-rank criteria #28in the caseofparallel solving of #28I + G#29s = t#29.

1996

"... In PAGE 32: ...Table 1 Low-rank criteria #28in the caseofparallel solving of #28I + G#29s = t#29. These results for parallel factoring of I+G and parallel #28I+G#29-solve are summarized in Table1 . Table 2 presents analogously obtained results for sequential LU-factoring and #28I + G#29-solve.... ..."

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### Table 4: Number of GMRES(5) iterations varying the threshold for a low-rank update of dimension 5 for the matrix ORSIRR1.

2002

"... In PAGE 7: ... Once this eigencomponent is removed by the rank-one update preconditioner both GMRES(40) and BiCGStab converge. To illustrate that the proposed updates should be used to improve an already e ective precon- ditioner, we report in Table4 the number of iterations when the threshold of ILU(t) is relaxed making the original preconditioner less and less e cient. We see that, in that case, the update will only improve the convergence up to a certain level above which it does not have any e ect.... ..."

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### Table 3.4: Number of GMRES(5) iterations varying the threshold for a low-rank update of dimension 5 for the matrix ORSIRR1.

2002

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### Table 4: Number of GMRES(5) iterations varying the threshold for a low-rank update of dimension 5 for the matrix ORSIRR1.

"... In PAGE 7: ... Once this eigencomponent is removed by the rank-one update preconditioner both GMRES(40) and BiCGStab converge. To illustrate that the proposed updates should be used to improve an already effective precon- ditioner, we report in Table4 the number of iterations when the threshold of ILU(t) is relaxed making the original preconditioner less and less efficient. We see that, in that case, the update will only improve the convergence up to a certain level above which it does not have any effect.... ..."

### Table 1: Image reconstruction method summary show- ing the estimate error, En, for the low-rank, keyhole, and adaptive framework methods.

"... In PAGE 2: ...Table 1: Image reconstruction method summary show- ing the estimate error, En, for the low-rank, keyhole, and adaptive framework methods. Theoretically Optimal Inputs For each case given in Table1 , the minimization of En requires a subspace identification. Specifically, the min- imization of En is analogous to the determination of the right singular vectors of a matrix, [1].... In PAGE 2: ... Thus, the optimal input vectors are not realizable. However, estimates formed from input vectors implied by Table1 provide a theoretical bound on the estimate quality for a given image reconstruction method. Furthermore, the fact that An changes over the course of the sequence implies that for the best image estimate quality, the inputs Xn must change for each image as well.... ..."

### Table 2 Low-rank criteria #28in the case of sequential solving of #28I + G#29s = t#29.

1996

"... In PAGE 32: ... These results for parallel factoring of I+G and parallel #28I+G#29-solve are summarized in Table 1. Table2 presents analogously obtained results for sequential LU-factoring and #28I + G#29-solve. If the symbol o in the restrictions on m #2857,58#29 is replaced with O, then instead of #2853#29 we will have t B = O#28t D + t m #29: #2859#29... ..."

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### Table 7. Regression analysis of contract design: separating research firms with high and low reputation underwriters High Rank Low Rank High Rank Low Rank Pooled

2007

"... In PAGE 32: ... In other words, the high rank of their underwriter should reduce the uncer- tainty about their type and render the termination and broader access rights more dispensable. In Columns 1 and 2 of Table7 , we find that the effects are instead larger and significant only among research firms with the highly ranked underwriters. The result is robust to the inclu- sion of year and firm fixed effects (Columns 3 and 4), though the significance of the coefficient estimate of interest in the high-rank sample diminishes.... ..."

### Table 4. Low Rank Approximation by Partition

2006

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