### Table 3.1 A summary of the numerical stability for di erent approximations to derivatives and the Birkho -Rott integral

1998

Cited by 6

### Table 5.2: Numerically computed stability constant C in the cases d = 3 (top) and d = 4 (bottom)

2002

### Table 3: Prediction of Stability of Flow Based on Numerical Simulation

"... In PAGE 3: ... Figure 2: Stable flow profile Figure 3: Unstable flow profile RESULTS AND DISCUSSIONS Numerical simulations were performed for flow parameters that correspond to various values of Ohnesorge and Capillary Numbers. The results are tabulated in Table3 . The Reynolds number in these simulations ranges from 0.... ..."

### Table 3. Evaluation of numerical stability for optimal three view triangulation. We compare the estimation error in 3D placement of the point. The combined svd and eigenvalue method yields an improvement in numerical precision by approximately a factor 106 over the state-of-the-art method.

"... In PAGE 7: ... The methods have been compared on 30.000 test cases and the errors are shown in Table3 and Figure 3. In this example the precision is improved by approxi- mately a factor 106.... ..."

### Table 2. Evaluation of numerical stability for relative pose for reg- ular cameras with unknown focal length. We compare the estima- tion error in relative focal length. The combined svd and eigen- value method yields an improvement in numerical precision by approximately a factor 105 over the state-of-the-art method.

### Table 9 Example 5, Numerical di erentiation using a standard Tikhonov method with rst-order stabilizer. /h cpu time alpha

1994

Cited by 1

### Table 1 Stability and convergence rates of rotational schemesa

"... In PAGE 33: ... In short, for all three classes of projection schemes, their rotational versions should always be preferred over the stan- dard versions. We now summarize in Table1 the main results related to the rotational forms of the pressure-correction methods, velocity-correction methods, and consistent splitting methods. References [1] Y.... ..."

### Table 1 Numerical behavior of the algorithms for the 1-2-2 system

"... In PAGE 2: ... The algorithms tested for this first set of simulations were the RLS and FTF algorithms found in [2], and the new inverse QR-RLS, QRD-LSL and symmetry-preserving RLS algorithms. Table1 compares the numerical stability of the different algorithms for multichannel ANC systems. From Table 1, it is clear that the RLS and FTF algorithms developed for multichannel ANC systems are numerically unstable, as previously reported in [2].... In PAGE 2: ... Table 1 compares the numerical stability of the different algorithms for multichannel ANC systems. From Table1 , it is clear that the RLS and FTF algorithms developed for multichannel ANC systems are numerically unstable, as previously reported in [2]. Although it is obtained from a slight modification to the numerically unstable RLS algorithm, the symmetry-preserving RLS algorithm was found to be stable (unless a very low value of forgetting factor such as 0.... ..."

### Table 3: Summary of Random Tree algorithms. The top three are based on linear algebra, the bottom six on random walks, and the middle one combines both techniques. The A subscript appears in the running time and space requirements of the algebraic algorithms since the operations being counted are arithmetic. In the absence of information on the numerical stability of these algorithms, it may be advisable to use exact arithmetic. Of the random walk algorithms, the top three are in the passive setting and the bottom three are in the active setting. All Markov chain parameters (which are de ned in Table 2) refer not to the Markov chain on the space of trees, but to the random walk on the graph. Quantities with over-bars and tildes refer to G (no self-loops added) and e G (self-loops added to make the graph out-degree regular), respectively.

1998

"... In PAGE 12: ... This Markov chain is known to randomize in polynomial time [22] [24], but when it is specialized to sampling trees, the algorithm fails to be competitive with the other tree algorithms. Table3 summarizes this history. 2.... In PAGE 37: ... Open Problems The main open question is, how well can one solve the Random State and Random Tree problems in the active setting? In particular, is it possible to solve the Random State problem more quickly than the mean hitting time ? Aldous gives a lower bound [1], but it is not clear how these bounds compare. There are quite a few maximal elements in the partial order of algorithms for the Random Tree problem ( Table3 ); an algorithm that runs in time O( ) for general graphs (rather than time O(e )) would reduce this number to two. Perhaps further progress could be made by combining random walk and algebraic techniques as done in [54].... ..."

Cited by 70

### Table 3: Summary of Random Tree algorithms. The top three are based on linear algebra, the bottom six on random walks, and the middle one combines both techniques. The A subscript appears in the running time and space requirements of the algebraic algorithms since the operations being counted are arithmetic. In the absence of information on the numerical stability of these algorithms, it may be advisable to use exact arithmetic. Of the random walk algorithms, the top three are in the passive setting and the bottom three are in the active setting. All Markov chain parameters (which are de ned in Table 2) refer not to the Markov chain on the space of trees, but to the random walk on the graph. Quantities with over-bars and tildes refer to G (no self-loops added) and e G (self-loops added to make the graph out-degree regular), respectively.

1998

"... In PAGE 12: ... This Markov chain is known to randomize in polynomial time [22] [24], but when it is specialized to sampling trees, the algorithm fails to be competitive with the other tree algorithms. Table3 summarizes this history. 2.... In PAGE 37: ... Open Problems The main open question is, how well can one solve the Random State and Random Tree problems in the active setting? In particular, is it possible to solve the Random State problem more quickly than the mean hitting time ? Aldous gives a lower bound [1], but it is not clear how these bounds compare. There are quite a few maximal elements in the partial order of algorithms for the Random Tree problem ( Table3 ); an algorithm that runs in time O( ) for general graphs (rather than time O(e )) would reduce this number to two. Perhaps further progress could be made by combining random walk and algebraic techniques as done in [54].... ..."

Cited by 70