### Table 4.4 presents the total memory requirements of the two approaches for computing the Jacobian of the MINPACK-2 problems for the case of n = 160; 000. In addition to the notation introduced in Table 3.2, we use MfJg to denote the memory requirements of the COMPRESSED approach, which includes the memory needed for the graph-coloring computa- tion, and MfJSparseg to denote the memory requirements of the SPARSE approach. For each problem, the ratio MfJg=MfFg remains constant for all n. Hence, Table 4.4 is a su cient summary of all the memory results. As mentioned in Section 3.1, the NONSPARSE mode of ADIFOR tends to augment memory requirements of the function computation linearly. In the case of the compressed Jacobian computations the augmentation factor is the chromatic number, p. However, since the graph-coloring algorithm also introduces additional memory requirements proportional to nnz(f0(x)), the MfJg=MfFg ratios in Table 4.4 are larger than the corresponding p values in Table 4.2, and we have

### Table 4.4 presents the total memory requirements of the two approaches for computing the Jacobian of the MINPACK-2 problems for the case of n = 160; 000. In addition to the notation introduced in Table 3.2, we use MfJg to denote the memory requirements of the NONSPARSE approach, which includes the memory needed for the graph-coloring computa- tion, and MfJSparseg to denote the memory requirements of the SPARSE approach. For each problem, the ratio MfJg=MfFg remains constant for all n. Hence, Table 4.4 is a su cient 18

1996

Cited by 5

### Table 2 Clustering coeSOcients of the market graph

2004

### Table 1: Event probabilities for causal structures Event Graph 0 Graph 1 Graph 2

2004

Cited by 4