### Table 2: Timings for fast and direct velocity evaluation methods with NT trian- gles. Asterisks denote timings obtained by extrapolation for the direct method.

"... In PAGE 31: ...6 Numerical results We now present numerical results which show that our algorithm achieves con- siderable speedups over direct evaluation. Table2 gives the result of fast and direct velocity evaluations for uniformly distributed random vortices in [?1; 1]2 with random ! values uniformly distributed on [?1; 1]. We take q = 0:2 and = 10?3, which requires p = 10 with r = 1.... ..."

### Table 2: Running times in milliseconds for direct evaluation, fast Gauss transform and improved fast Gauss transform in three di- mensions.

2003

"... In PAGE 6: ...etween 0 and 1. The bandwidth of the Gaussian is h =0.2. We set the relative error bound to 2% which is reasonable for most kernel density estimation, because the estimated density function itself is an approximation. Table2 re- ports the CPU times using direct evaluation, the original fast Gauss transform (FGT) and the improved fast Gauss trans- form (IFGT). All the algorithms are programmed in C++ and were run on a 900MHz PIII PC.... ..."

Cited by 36

### Table 2.16 Run times in seconds for direct form lter Signal Simulation DBT Approximate method Fast Method

1999

### Table 4: Distributions and their evidence Therefore incremental calculation of Bayes factors can be done when searching through the space of models, or when doing Gibbs sampling through the space. This result again applies in general to DAGs, undirected graphs and chain graphs. It has been used in fast learning algorithms for trees and DAGs [Bun91b, Bun91d, CH92]. The method in general requires decomposing the models so the parameters form their nest aposterior independent sets, and then comparing the di erence in the factorization of evidence. Details of the corresponding property for undirected graphs are given in [DL93].

1994

"... In PAGE 55: ...re given later in Section 6. Standard reference priors for these distributions [BT73] can be used. Denote the corresponding su cient statistics as n1;j, the number of data where var1 = j, and n2;jji, the number of data where var2 = j and var1 = i. Then the rst two terms of the evidence for model M1, read directly from Table4 , can be written down as: p(var1; jM1) = Beta(n1;0 + 1;0; n1;1 + 1;1) Beta( 1;0; 1;1) ; p(var2; jvar1; ; M1) = Beta(n2;0j0 + 2;0j0; n2;1j0 + 2;1j0) Beta( 2;0j0; 2;1j0) Beta(n2;0j1 + 2;0j1; n2;1j1 + 2;1j1) Beta( 2;0j1; 2;1j1) Assume the variables x1 and x2 are Gaussian with means given by 1j0 when var1 = 0; 1j1 when var1 = 1; 2j0;1 + 2j0;2x1 when var1 = 0; 2j1;1 + 2j1;2x1 when var1 = 1: and variances 1jj and 2jj respectively. In this case, we split the data set into two parts, those when var1 = 0, and those when var1 = 1.... In PAGE 56: ...Learning with Graphical Models 56 The evidence for the last two terms can now be read from Table4 . This becomes: p(x1; jvar1; ; M1) = Y j=0;1 p 0;1jj n1;j=2p 0;1jj + n1;j ?(( 0;1jj + n1;0)=2) ?( 0;1jj=2) 0;1jj=2 0;1jj 0;1jj + s2 1jj + 0N 0 + N (x ? 0;1jj)2 ( 0;1jj+n1;j)=2 ; p(x2; jx1; ; var1; ; M1) = Y j=0;1 det1=2 0;2jj n1;j=2 det1=2 2jj ?(( 0;2jj + n1;0)=2) ( 0;2jj+n1;j)=2 2jj ?( 0;2jj=2) 0;2jj=2 0;2jj : The nal simpli cation of the model is given in Figure 45.... ..."

Cited by 189

### Table 3.1: Comparison between the described Ewald method, the direct method and the regular Ewald method. (The R in the direct method stands for the radius, in basic cell diameters, of a sphere within which we took image cells into account. P is the expansion depth in the Fast Multipole Method.)

### TABLE I GAUSSIAN PROCESS PARAMETERS

2001

Cited by 90

### TABLE I GAUSSIAN PROCESS PARAMETERS

2001

Cited by 90

### TABLE 1: Comparison of Exact and DSD-Determined Parameters for a Synthesized Time Signal Consisting of a Sum of Exponentially Decaying Oscillations, with Known Frequencies, Amplitudes, Phases, and Damping Constantsa

### Table 2: Performance of the fast evaluation method (d = 2). The N centers coincide with the M evaluation points and are uniformly distributed in the unit square. The table shows times in seconds for the approximate and direct evaluation of the Inverse Multiquadric interpolants.

2004

"... In PAGE 14: ... Test Problem 2. The second test case is two-dimensional Inverse Multiquadric interpolation ( Table2 ). The evaluation points coincide with the centers and are uniformly distributed on the unit square.... In PAGE 15: ...Figure 1: Graphic representation of Table2 , comparing the performance of the direct and the fast method. Dotted line is the fast method.... ..."