### Table 3: Execution times for vector-matrix multi- plication

"... In PAGE 3: ...Table 3: Execution times for vector-matrix multi- plication Table3 shows the obtained execution times in microseconds. The parameter n denotes the number of multiplications performed.... ..."

### Table 5.2 Computational effort for vector-matrix multiplication.

1997

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### Table 5.2 Computational effort for vector-matrix multiplication.

1997

Cited by 20

### Table IV. Computational Effort for Vector-Matrix Multiplication (in Seconds)

### Table IV. Computational E ort for Vector-Matrix Multiplication (in Seconds)

2000

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### Table 4: Computational e ort for vector-matrix multiplication (time in seconds).

"... In PAGE 21: ... These observations are con rmed by our running example. Table4 gives the number of oating point multiplications performed by the algorithms we introduced and their execution times to compute ^ x ^ R, or ^ xT ^ RT ;T , where ^ R is given by Eq. (3).... In PAGE 31: ... We performed iterations using the absolute convergence criterion jj old ? newjj1 lt; 10?8. As already anticipated in Table4 , algorithms Pot-Sh-JCB and Pot-RwCl-JCB fail due to insu cient memory with the second decomposition, while Pot-Cl-GSD could be run, but with an unacceptable amount of overhead; the same holds for Act-Sh-JCB, where the space requirements are clearly dominated by the auxiliary vector ^ aux of size n. We observe that the two decompositions result in di erent state orderings, which in turn a ect the convergence of Act-Cl2-GSD.... ..."

### Table 4. Spectral Parameters for 3D (Discrete) Case: (a) Original Set of Spectral Parameters for Particular Spectral Components of Synthetic 3D Spectrum and Corresponding Group Parameters (b) after GHOST Condensation of Original Distribution and (c) after GHOST Condensation of HEO 4D-Projectionsa

2005

"... In PAGE 7: ... However, the accuracy for the determination of the contributions of the three spectral components reduces to 5-10% (previously 1-2%). The group at the lowest order parameter was found with larger contribution (group index 1, Table4 c) as compared to the original one (comp. index 1, Table 4a).... In PAGE 7: ... The group at the lowest order parameter was found with larger contribution (group index 1, Table 4c) as compared to the original one (comp. index 1, Table4 a). This is again an example of discrete group confirmation during the slicing process.... ..."

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### Table 5. Spectral Parameters for 2+13D (Discrete + Quasi-Continuous) Case: (a) Original Set of Spectral Parameters for Particular Spectral Components of Synthetic 2+13D Spectrum and Corresponding Group Parameters (b) after GHOST Condensation of Original Distribution and (c) after GHOST Condensation of HEO 4D-Projections (Lowest Slice Only)a

2005

"... In PAGE 8: ... The third example shows a synthetic EPR spectrum with 15 spectral components. In this spectrum, two spectral components were constructed with significantly higher contribution relative to the others (see Table5 a). This 2+13D spectrum is an example of a combined discrete and quasi- continuous spectrum.... In PAGE 8: ... This arises because some of the groups of original points are close to each other and fulfill the neighboring condition of eq 7. Moreover, the GHOST condensation of 4D-projections gives an even more continu- ous picture; it detects the presence of two large groups of solutions on the lowest slice ( Table5 c and Figure 8b), covering the positions of all the spectral component points. Another feature can be seen in the GHOST diagram of 4D-projections of the 2+13D spectrum (Figure 8b).... In PAGE 8: ... Within the group (at the lowest slice) at low order parameter another group of solutions with higher density (at the higher slices) is present (see Figure 8b), which is the consequence of the presence of a spectral component with a high proportion in the original distribution (comp. index 1, Table5 a). This spectral component with a contribution of 20% is merged Table 3.... In PAGE 9: ...2-5, Table5 a) into one group (group index 1, Table 5b) in the GHOST condensation of the original distribution. In the GHOST condensation of the 4D-projections the correspond- ing discrete group is found with a contribution of 24% (originally 20%) at a higher slice (Figure 8b) but merged with several solutions with lower density to give a continuous group with a contribution of 58% at the lowest slice (group index 1, Table 5c; originally 61%).... In PAGE 9: ...2-5, Table 5a) into one group (group index 1, Table 5b) in the GHOST condensation of the original distribution. In the GHOST condensation of the 4D-projections the correspond- ing discrete group is found with a contribution of 24% (originally 20%) at a higher slice (Figure 8b) but merged with several solutions with lower density to give a continuous group with a contribution of 58% at the lowest slice (group index 1, Table5 c; originally 61%). Accordingly, the slicing process of this group of points obviously results in a discrete group superimposed on a continuous group.... In PAGE 9: ... Accordingly, the slicing process of this group of points obviously results in a discrete group superimposed on a continuous group. The group with a contribution of 42% (group index 2, Table5 c) is also found on the lowest slice, but the distribution of the points is not so wide (originally this should be a discrete group of 30% superimposed on 9% background). This can be seen from Table 7c, by comparing the second moment for group 1 and 2.... ..."

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### Table 19: Performance data for matrix{vector and vector{matrix multiplication on dif- ferent Connection Machine system CM{200 con gurations. 64{bit precision. 37

1993

"... In PAGE 37: ...0. A summary of the performance of the matrix{vector (M-V) and vector{matrix (V-M) routines are given in Table19 and in Figure 23.... ..."

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### Table 1: Performance data for matrix{vector, vector{matrix, and rank{1 updates on di erent Connection Machine system CM{200 con gurations. 64{bit precision. 5 Performance

1994

"... In PAGE 17: ... 64{bit precision. 5 Performance Table1 and Figures 7, 8 and 9 give the performance of the matrix{vector, vector{matrix, and rank{1 update routines for square matrices. For real operands, the peak performance of the three algorithms in 64{bit precision is 4500 M ops/s, 5825 M ops/s, and 3266 M ops/s, respectively.... ..."

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