### Table 5: Test of CG{method with discrepancy principle for n = 16 ( quot; = 0:01, neps = 0:023135)

### Table 6: Test of CG{method with discrepancy principle for n = 24 ( quot; = 0:01, neps = 0:028795)

### Table 1: Tests of the General Commutativity Principle (GCP)

2003

"... In PAGE 5: ... For our 6 subjects, that resulted in a total of 24 tests. The outcome of these tests is given in Table1 . It is obvi- ous, that the decibel differences produced by adding a difference subsequent to generating a loudness ratio, as opposed to applying the two operations in the reverse order, are relatively small, the average discrepancy amounting to less than a decibel.... In PAGE 5: ...ubjects sometimes distinguish perceptual ratios and differences (e.g. Schneider, 1980; Birnbaum, 1982). Note, however, that the deviations from the Generalized Commutativity Principle are small, and that the direction of the effect (positive differences in Table1 ) is the opposite of what would be intuitively expected when numerical ratios and differences are concatenated (see Figure 1). The present study further stresses the importance of distinguishing between numeral ratios or differ- ences (i.... ..."

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### Table 4. Average Relative Error relerrres of the Residual Norm k (AAT + I)?1bk2.

"... In PAGE 21: ... Table4 presents the average relative error of the residual norm for each test case. Morozov apos;s discrepancy principle and the Gfrerer/Raus-method give excel- lent estimates for kek2.... ..."

### Table 5. Average Number of Lanczos Iterations k.

"... In PAGE 21: ... The computational cost of our regularization techniques is proportional to the number k of Lanczos iterations. In Table5 we give an overview of the av- erage number of required iterations. Morozov apos;s discrepancy principle and the Gfrerer/Raus-method require roughly the same number of iterations to con- verge.... ..."

### Table 3. Average Relative Error relerr of the Regularization Parameter .

"... In PAGE 20: ...Let be an approximation to computed by one of our approximation methods. Then we de ne the relative error relerr := j ? j min( ; ): Table3 presents the average relative errors for all the test cases. Our approximation techniques work extremely well for Morozov apos;s discrepancy principle and the Gfrerer/Raus-method.... ..."

### Table 3. k =0:1 0:25k 1

"... In PAGE 9: ... As the rst guess we choose a0 =1+0:4(7t2 10t4 +3t6). It can be argued that a0 ay 2 R(F0(ay) F0(ay)): In Table3 we summarize the numerical results obtained by using Rule 2.1, and the discrepancy principle (7) with k =0:1 0:25k 1.... ..."

### Table 7: Statistical summary for Discrepancy Discrepancy

"... In PAGE 7: ...1.4 Discrepancy Table7 shows statistical summary for discrepancy. In the remaining, this Section presents discrepancy with respect to ODC categories (Table 8), programming languages (Table 9), expertise (Figure 9), and seeded defects (Figure 10), respectively.... ..."

### Table 2: Mixed discrepancies

"... In PAGE 7: ... Table 1 shows the pure discrepancies: discrepancies that only affect one of the three information categories. Table2 shows the mixed discrepancies, where two or three of the categories are affected. Pure discrepancies are less interesting than mixed ones, as their cause can be traced to some kind of spelling or typographical error.... ..."

### Table 4: Analysis of discrepancies

2007

"... In PAGE 12: ...It can be seen in Table4 that the percentage of banks precisely classified (k = 0) with the ordered logistic model built using the entire data set is equal to about 37%, while the average number ... In PAGE 22: ...00% Average Difference Between Fitch and LAD Ratings 0.98 categories We have conducted 20 experiments (10 times 2-folding) to evaluate the robustness and extendability of the ordered logistic regression rating model ( Table4 ) and the LAD rating model (Table 10). These 20 experiments can also be used to check whether the rating discrepancy between the LAD and the Fitch ratings and that between the ordered logistic regression and the Fitch ratings differ from each other in a significant way under the assumptions that the paired differences are independent and identically normally distributed.... ..."

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