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These multipliers can be found numerically using ellipsoid or interior point method with a complexity [17, 34].
However, it is computationally complex to solve more than one Lagrangian multiplier shown in Eq. (13), these multipliers can be found numerically using ellipsoid or interior point method with a polynomial time complexity o(N3) [25].
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This value is found numerically using Ridder's method [ 50].
Since we have not found a closed-form inverse to this relationship, the appropriate the value of p was found numerically using a binary search over numbers in [0,1].
Incorporating cortical diffusion into the model is straightforward, though solutions now need to be found numerically.
This minimal model is mathematically unique and can be found numerically (Schneidman et al., 2003).
This solution was found numerically by using the original problem formulation (1.9a - 1.9b 1.9a - 1.9b
The smoothing improvement factor is defined as Sigma= frac{epsilon_{mathrm{filt}}}{epsilon_{x}}, (25) where (epsilon_{x}) is the smoothed MSE (see equation (24)) and (epsilon_{mathrm{filt}}) is the optimal filtered MSE error found numerically using the optimal Kalman-Bucy filter covariance matrix [20].
Stillinger [628] found numerically that the perturbation coefficients (not found numerically using perturbation theory but by fitting variationally calculated eigenvalues) are eventually all positive, so there is a singularity on the positive real axis at (rho ).
For the ML estimator the maximum of the likelihood (Eq. 2) was found numerically (for M>2) using Newtons method.
For an elliptic cross-section of a uniform rod the stability region is found numerically with the use of the Galerkin method and the exact numerical approach.
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