### Table 3. Comparison of models for the non-linear function approximation.

2003

"... In PAGE 7: ...and validation data set, respectively. Table3 contains comparison results of di erent models for the static function approximation and provides, in addition, re- sults achieved with the neural tree model developed in this paper. It is obvious that the proposed neural tree model worked well for generating an approxi- mating model of the static non-linear system.... ..."

### Table 3: Results of simulations for function approximation

"... In PAGE 6: ... The FNN is based on hidden neurons with logistic activations and on a linear output neuron. Comparative results are exhibited in Table3 . There is a remarkable improvement of the BBP algorithm when the nonmonotone learning strategy is used; the BBP algorithm has a success rate of 79.... ..."

### Table 4: Results of simulations for function approximation

1998

"... In PAGE 6: ...rrors (over 20 input/output sets) becomes less than the error goal 0.1. The network is based on hidden neurons of logistic activations with biases and on a linear output neuron with bias. Comparative results are exhibited in Table4 . Once again, the BBP method exhibited the best performance and had a very high success rate 74%.... ..."

Cited by 1

### Table 3 Comparison of model performance for the non-linear function approximation

2003

"... In PAGE 14: ... 10(d)) by using both rule elimination and rule combination approaches presented in Section 4. The performance of the simpliFFed models and the comparison with models developed in [4,8,17] are displayed in Table3 . It can be seen that the proposed fuzzy models not only improved its interpretability but also increased the model accuracy.... ..."

### Table 3: Learning of neuro-fuzzy function approximators.

1995

"... In PAGE 38: ... After that, the most significant basis functions are selected to the final system using the OLS. Summary Table3 collects learning schemes used in several recently introduced neural fuzzy inference systems. Their training methods differ very much from each other and no comparison of methods has been presented.... ..."

### Table 9: Generating functions for approximate MLS approximation in IRs.

2005

"... In PAGE 64: ... The graphs on the right show the execution times in seconds for direct summation (solid lines) and FFT summations (dashed lines). The colors correspond to the three di erent types of kernels listed in Table9 below. The red curves correspond to the Gaussians (listed in the O(h2) column), green curves to the function in the O(h4) col- umn (Gaussian multiplied by a linear Laguerre polynomial), and blue curves to those in the O(h6) column (Gaussian multiplied by a quadratic Laguerre polynomial).... In PAGE 64: ... For the one and two-dimensional experiments this cross-over point occurs much earlier and is not detectable in the g- ures. The polynomial terms in Table9 are given by generalized Laguerre polynomials with radial arguments.... ..."

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### Table 4. Performance of linear and nonlinear value function approximations against a deterministic rolling horizon procedure, from Topaloglu and Powell, 2000

in Contents

2002

"... In PAGE 68: ... As with single commodity problems, we can obtain integer solutions as long as we use piecewise linear value function approximations. Table4 demonstrates the effective- ness of the techniques on both deterministic problems (compared against the results of an LP solver) and stochastic problems (compared against deterministic rolling horizon approxi- mations). Again, we see that the techniques provide near optimal solutions on deterministic... ..."

### Table 2: obtained extents from approximated basis functions and approximated charge distributions. The estimated upper bound can be reduced by using the second algorithm.

2004

"... In PAGE 38: ...Table2 : CH3125I fragments as a function of total charge Q, DFT B3LYP, for different basis sets Q SVP/ecp-46-mwb SVPall TZVP/ecp-46-mwb TZVPall +1 3CH3Te+ 3CH3Te+ 3CH3Te+ 3CH3Te+ +2 2CH3Te2+ 2CH3Te2+ 2CH3Te2+ 2CH3Te2+ +3 1CH3Te3+ 1CH3Te3+ 1CH3Te3+ 1CH3Te3+ +4 2CH+ 2 + 3Te2+ + H+ 2CH+ 2 + 3Te2+ + H+ 2CH+ 2 + 3Te2+ + H+ 2CH+ 2 + 3Te2+ + H+ +5 1CH+ + 3Te2+ + 2H+ 1CH+ + 1Te2+ + 2H+ 3CH+ + 3Te2+ + 2H+ 1CH+ + 3Te2+ + 2H+ +6 2C+ + 3Te2+ + 3H+ 1CH+ + 2Te3+ + 2H+ 3C + 2Te3+ + 3H+ 2C+ + 1Te2+ + 3H+ +7 2C+ + 2Te3+ + 3H+ 2C+ + 2Te3+ + 3H+ 2C+ + 2Te3+ + 3H+ 3CH+ + 1Te4+ + 2H+ +8 1C2+ + 2Te3+ + 3H+ 1C2+ + 2Te3+ + 3H+ 2C+ + 1Te4+ + 3H+ 2C+ + 1Te4+ + 3H+ +9 1C2+ + 1Te4+ + 3H+ 1C2+ + 1Te4+ + 3H+ 1C2+ + 1Te4+ + 3H+ 1C2+ + 1Te4+ + 3H+ +10 2C3+ + 1Te4+ + 3H+ 1C2+ + 2Te5+ + 3H+ 1C2+ + 2Te5+ + 3H+ 1C2+ + 2Te5+ + 3H+ +11 2C3+ + 2Te5+ + 3H+ 2C3+ + 2Te5+ + 3H+ 2C3+ + 2Te5+ + 3H+ 2C3+ + 2Te5+ + 3H+ Figure 2: Picture sequence of C2H5125Te as a function of charge... In PAGE 43: ... The only exception was found for CH3125Te5+ for TZVP/ecp-46-mwb, where one additional proton appears to be bound to the carbohydrate fragment. Table2 give the obtained fragmentations of CH3125I, using the exchange functional B3LYP. All basis sets give identical fragmentation patterns for systems up to a total charge of +5, except of the different multiplicities for the CH3125I5+ systems.... ..."

### Table 2: Comparative Results for the Function Approximation Problem

"... In PAGE 5: ... In the same problem, the Silva#7BAlmeida apos;s method fails to converge in 44 out of the 100 runs, due to convergence to undesired local extrema. For the same reason, this method converges only 11 times #28see Table2 #29 in the function approximation problem. In this problem, the Global Quickprop outperforms the classical method in the number of successful runs.... ..."

### Table 1: Control parameters for function approximators in CES.

1998

"... In PAGE 16: ... The second group of parameters are control parameters which can be set by the programmer. Currently, CES offers the control parameters listed in Table1 , which can be modified if the initial default parameters are inappropriate, using the command faset: faset( amp;fa-name, param-name, value); Here fa-name denotes of the name of the function approximator, param-name the name of the parameter according to Table 1, and value the desired parameter value. For example, the code... In PAGE 16: ... The second group of parameters are control parameters which can be set by the programmer. Currently, CES offers the control parameters listed in Table 1, which can be modified if the initial default parameters are inappropriate, using the command faset: faset( amp;fa-name, param-name, value); Here fa-name denotes of the name of the function approximator, param-name the name of the parameter according to Table1 , and value the desired parameter value. For example, the code... ..."

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