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The augmented Lagrangian parameter is estimated by an automatic analysis of the discretization matrix resulting from the approximation of the momentum equations.
The residual error at the output of the PA consists of two terms resulting from the approximation errors in the amplitude and phase LUTs.
The nonlinear equation resulting from the approximation of the boundary conditions is solved by the Newton's method, using Multidimensional Root-Finding routines from the GNU Scientific Library GSLL).
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As starting values for λ and the two μ parameters, the posterior modes resulting from the Laplace approximation were used.
It is of fundamental importance to note here that the crucial task in applying the Galerkin-spectral Bernstein approximations is how to choose an appropriate basis for such that the linear system resulting from the Bernstein-Galerkin approximation to (4.4) is as simple as possible.
A two-level additive Schwarz preconditioner is proposed for solving the algebraic systems resulting from the finite element approximations of space fractional partial differential equations (SFPDEs).
Although we see that this approximation converges, the peaks often do not occur at the correct locations, as opposed to the approximations resulting from the zero-pole interpolation (compare to Figure 8).
Two different approaches are used for the estimation of the approximation error resulting from the OCFE solution.
Thus, the following sections discuss the non-zero-offset extension of the two-step method, the approximations resulting from the application to vertically variable velocity fields, and finally the distortion effects on the aperture of the migration operators.
In this scenario, characterization of historical events estimated from genetic data are crude approximations resulting from the influence of reproductive patterns, isolation, genetic mutation, population admixture, drift, founder effect, and expansion and divergence lag times.
Then, a decentralized control scheme is developed as function of the local area state variables and those resulting from the overlapped states which represent an approximation of the interconnection variables.
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