### TABLE I ASYMPTOTIC TOTAL OVERHEAD EXPRESSIONS.

2002

Cited by 26

### TABLE I ASYMPTOTIC TOTAL OVERHEAD EXPRESSIONS.

2002

Cited by 26

### Table 2: Derivative Approximations. An important aspect to be considered is the validity of the asymptotic expression for the bias of the parameter estimate. In general, the bias may be expressed in series expansion with respect the sampling period h as: B(h) = C1h + C2h2 + C3h3 + O(h4) (9:2) with the coe cients Ci depending on both the process parameters and the deriva- tive approximation. When h tends to zero, the asymptotic expression can be considered:

### Table 1: Asymptotic limits for which analytic expressions for the preconditioned Fourier footprints of rst order matrix dissipation are obtained.

### Table 4.2: Accuracy of Asymptotic Expansion. TERMS EXPRESSION ERROR 1 0.57722 150.559

2001

### Table 2 collects the asymptotic expressions for the space (memory) and time (CPU secs) complexity of the different schemes. In the two first columns we isolate the dependency on the number of iterations n and in the last one we explicit the application dependencies. Let us note that the REM time complexity is high, being proportional to the square of the iteration numbers. Therefore the REM scheme for S-TABU is convenient only when the memory cost of a single configuration is very high with respect to the cost of storing a single move.

"... In PAGE 21: ... Table2 : Asymptotic requirements of CPU time and memory space for different tabu schemes. In Table 2, n denotes the number of iterations, N the problem size, f the function to be optimized and C(f, N) the computational cost for evaluating the neighborhood containing |S| points, a number depending on the problem size.... In PAGE 21: ...Table 2: Asymptotic requirements of CPU time and memory space for different tabu schemes. In Table2 , n denotes the number of iterations, N the problem size, f the function to be optimized and C(f, N) the computational cost for evaluating the neighborhood containing |S| points, a number depending on the problem size. The constant k0 is the cost of the single tracing step of REM, k1 is the average fraction of number of configurations evaluated in the neighbor- hood, D0 is the cost of a single fetch-and-test operation on the node of the digital tree, H0 and H1 depends on the specific hashing scheme (H0 in the case of storing the whole configuration, H1 in the case of storing a single compressed item).... ..."

### Table 1. Asymptotic transition probability in the generic case.

"... In PAGE 7: ... These conditions specify the global behaviour in the strip of the so-called Stokes lines, which are the level-lines Im ( ) = Im (zj), where zj is a zero of 13,19. The results of the analysis are given in Table1 when the above mentioned conditions are satis ed for one (and then necessarily unique) simple zero zj of . This case is generic.... In PAGE 8: ... The case of the avoided crossing leading to the Landau-Zener formula is important in Physics. The last row of the Table1 yields an asymptotic formula accurate up to exponentially small relative errors. The expressions e 1 and are de ned as e1 and with Hq in place of H (see comment 1 on the adiabatic theorem).... ..."

### Table 1: Alternative expressions for

"... In PAGE 16: ... 5 ANALYSIS OF CONVERGENCE We shall examine the local convergence of Methods 1, 3 and 4 by studying the application of one or more modi ed steps in each case, on the assumption that the preceding step (that is, the step producing xi+1) was unmodi ed. It then follows that the latest error, quot;i+2, is related to the prevous errors by (compare equations (2) and (3)): quot;i+2 = f fi?1 quot;i+1 ? fi+1 quot;i?1g=f fi?1 ? fi+1g = quot;i?1 quot;i+1 fi?1 ? fi+1 fi?1 quot;i?1 ? fi+1 quot;i+1 : (10) In all three of the new methods, it is evident (using the relations (6) and (9)) that 1 asymptotically (see Table1 ). Hence, we choose to express in the form = 1 + = ; (11) where we assume (and will demonstrate in each case) that = O( quot;); = O(1); (12) where quot; = max(j quot;i?1 j; j quot;i j): (13)... ..."

### TABLE III CONTRIBUTIONS TO THE ASYMPTOTIC ONE-STEP PARAMETER PREDICTION ERROR tr4080 41 WHEN FIR MODELS WITH 33 61485849 OF ORDER 77 ARE TRACKED BY WLMS IN EXAMPLE 2. THEORETICAL PREDICTIONS FROM RELEVANT EXPRESSIONS IN THEOREM 3(BOLD)ARE COMPARED WITH SIMULATIONS (ITALICS)

Cited by 2

### Table 2: This table is an adjunct to Table 1. It shows the expected number of nodes explored in the search tree divided by the number of steps in a preprocessing phase, for various image sizes and salience fractions. This expression shows that asymptotically, the expected amount of work is exponential in n. To predict at what point the computation will become unmanageable, we compute the expected amount of work for a variety of realistic situations (further details of the computation are given in [27]). We do not prove that the summation of EiXi converges, but we nd in practice that the terms become tiny for high values of i.

"... In PAGE 17: ... Table 1 shows the expected work of the system as n and k vary. Table2 shows the amount of work of the system divided by (2n)2 log(2n). This tells us roughly the proportion of the system apos;s work that is spent in search, as opposed to xed overhead, although one step of overhead is not directly comparable to one step of search.... ..."