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We solve the problem by sample average approximation in combination with dual decomposition.
In contrast our method, using the linear noise approximation in combination with numerical optimisation, took 25 min to converge.
To get reliable results and to enhance the accuracy of Bayesian predictive measures (i.e. DIC and logarithmic CPO values), the full Laplace approximation in combination with the so-called GRID integration scheme was chosen as the strategy for deterministic approximation of the latent Gaussian field and the posterior marginals of the hyperparameters.
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We then propose a hybrid approach employing the approximation algorithm in combination with {0,1} LP.
Different approximation models are applicable in combination with the developed optimization technique.
The mass conservation properties inherent to finite volume-based methods motivate a DFVE scheme for the approximation of the Brinkman flow in combination with a RKDG method for the spatio-temporal discretization of the saturation equation.
In this paper, we present a novel modified version of Cox and Matthews fourth-order ETDRK scheme based on sub-diagonal Padé approximation to matrix exponential functions in combination with compact fourth-order finite difference scheme (in space) for direct integration of reaction diffusion problems with nonsmooth data.
Model-to-data fit in the current study was evaluated using the chi-square test [ 31] and root mean square error of approximation (RMSEA) [ 32] statistics in combination with the comparative fit index (CFI) and standardized root mean square residual (SRMR), which are accepted indicators of model-data fit [ 30, 33].
Their method is shown to achieve accurate results only in combination with an approximation of the interference statistics by a Gamma distribution.
An energy-based formulation that includes a polynomial Rayleigh Ritz approximation into the potential energy function, in combination with the Lagrange's method of undetermined multipliers, has been found very convenient for this type of problem.
More recently, the authors of [29 31] proposed the operational matrices of Riemann-Liouville fractional integration of Chebyshev, Laguerre, modified generalized Laguerre polynomials which are employed in combination with tau approximation for the numerical solution of linear FDEs on finite and semi-infinite intervals.
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