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In this work, we approximated the local truncation error using the τ-estimation procedure, which aims to compare the residuals on a sequence of grids with different spacing.
To that end we have approximated the local instantaneous FBA solution in a given lattice site using a precomputed lookup table (see Additional file 1: Section 1.2 for details).
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In this method, each sensor first determines a local set which approximates the local posterior density.
Different summation methods of multidimensional trigonometric Fourier series are adopted for approximating the local strain and stress in elastic periodic composites.
Investigating the form of equations (2) and (6), one can see that the accuracy of the Evans method is strongly related to how accurately equation (6) approximates the local derivative of J t).
Pseudopodial activities have also been identified by approximating the local curvature of the boundary using a closed polygon formed from a chain of nodes [ 4].
This leads to a discrete velocity gradient v i j m that approximates the local velocity gradient v ij = ∂ i v j in the continuum limit, where v(r ) denotes the velocity field.
The Hessian matrix ∂ 2 log p (x ) / ∂ x ∂ x T | x = ψ is set to the covariance matrix H, which approximates the local curvature in a neighborhood of ψ.
Heights of a large number of gravity points were interpolated from contour maps or approximated using the local sea surface.
Some gravity observations were carried out on benchmarks and triangulation points, but the heights of a large number of gravity points were interpolated from contour maps or approximated using the local sea surface.
Spatial variation of all physical fields (or of their Laplace transforms) at discrete time instants are approximated on the local boundary and in the interior of the sub-domain by means of the moving least-squares (MLS) method.
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