### Table 1: Values of R(e1) for di erent choices of quadratic irrationals e1 Figure 6 presents a plot of a typical sequence of iterates (xn; rn), n = 1; : : : ; 100; 000 for a non{periodic symmetric algorithm, corresponding to Corollary 3 (iii). This propery has the important consequence that a direct implementation of a symmetric algorithm, based on the application of the rule E0 n = An+Bn?En yields sub{exponential convergence (R = 1) due to numerical inaccuracies. In particular, this is the case for the GS algorithm, hence the usual recommendation to use the implementation (1). Note that among symmetric algorithms, R(e1) is minimum when e1 = apos;, the Golden Section. This follows from Corollary 2 and the fact that

in Analysis of Performance of Symmetric Second-Order Line Search Algorithms Through Continued Fractions

### Table 1: A comparison of public-key cryptosystems [16].

2004

"... In PAGE 2: ... The relative difficulty of solving that problem determines the security strength of the corre- sponding system. Table1 summarizes three types of well known public-key cryptosystems. As shown in the last column, RSA, Diffie-Hellman and DSA can all be attacked using sub-exponential algorithms, but the best known attack on ECC requires exponential time.... ..."

Cited by 11

### Table 1. A comparison of public-key cryptosystems [30]. Public-key system Examples Mathematical Problem Best known method for

"... In PAGE 2: ... The relative difficulty of solving that problem de- termines the security strength of the corresponding system. Table1 summarizes three types of well known public-key cryptosystems. As shown in the last column, RSA, Diffie- Hellman and DSA can all be attacked using sub-exponential algorithms, but the best known attack on ECC requires ex- ponential time.... ..."

### Table 2. Codewords of the subexponential code. k = 0 k = 1 k = 2

2003

"... In PAGE 2: ....2. Subexponential Code As in the case of the exponential-Golomb code, the codewords of the subexponential code can also be di- vided into groups and we use the number of 1s in the prefix as the group index. Table2 shows thecode- words of the subexponential code for run-lengths vary- ing from 0 to 10 with the code parameter k = 0, 1, 2. From the table, we can find that the size of group A0 is 2k.... ..."

### Table 3.7. Subexponential dfs. All of them are in S provided they have nite mean.

1998

Cited by 23

### Table 3.7. Subexponential dfs. All of them are in S provided they have nite mean.

1998

Cited by 23

### Table 1. Comparison of results between grids with and without diagonals. New results

1994

"... In PAGE 2: ... For two-dimensional n n meshes without diagonals 1-1 problems have been studied for more than twenty years. The so far fastest solutions for 1-1 problems and for h-h problems with small h 9 are summarized in Table1 . In that table we also present our new results on grids with diagonals and compare them with those for grids without diagonals.... ..."

Cited by 11

### Table 1{Performance bounds for zero propagation delay algorithms Class of Scheduling Range of Property P3 Property P2 Property P1 Algorithms Throughput k N k

1997

"... In PAGE 13: ...3 For gt; 12, S 6, and n 3, no scheduling algorithm in the class CONTIN- UOUS STATIC has any property P1{P4. Table1 summarizes the throughput and delay characteristics of the scheduling algorithms pre- sented in this and the previous section. The last three columns list the upper bounds for k N k,... ..."

Cited by 45

### Table 2: The beginnings of the new subexponential codes for a few parameter values. The codes can be extended to all non-negative values of n, and codes can be constructed for all k 0. In this table a midpoint ( ) separates the high-order (unary) part from the low-order (binary) part of each codeword.

1994

"... In PAGE 8: ...u + b + 1 = ( k + 1 if n lt; 2k; 2blog2 nc ? k + 2 if n 2k: Examples of this code appear in Table2 . It can easily be shown that for a given value of n, the code lengths for adjacent values of k di er by at most 1.... ..."

Cited by 9

### Table 2: The beginnings of the new subexponential codes for a few parameter values. The codes can be extended to all non-negative values of n, and codes can be constructed for all k 0. In this table a midpoint ( ) separates the high-order (unary) part from the low-order (binary) part of each codeword.

1994

"... In PAGE 6: ...u + b + 1 = ( k + 1 if n lt; 2k; 2blog2 nc ? k + 2 if n 2k: Examples of this code appear in Table2 . It can easily be shown that for a given value of n, the code lengths for adjacent values of k di er by at most 1.... ..."

Cited by 9