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We also study some results on best approximation via common fixed point theorems.
Real time visualization is achieved by incrementally computing a polygonal approximation via the Marching Cubes algorithm.
Nevertheless, the particle-based approximation via nonparametric representation makes probabilistic methods acceptable for the inference in sensor networks.
Then the approximation via the convex hull is formulated as conv V) and is the V-representation.
However, particle-based approximation via nonparametric belief propagation (NBP), proposed by Ihler et al. [2 4], makes BP acceptable for inference in sensor networks.
We assume in our implementation that (21) is still a circular symmetric complex normal PDF [31], which is enforced by the approximation via (23).
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Furthermore, there is not a convergence of the shape of proposal to the shape to target, but only local approximations via b-spline interpolation.
In the following, using a 1D model, the pre-stack inversion based on different order approximations via nonlinear variable metric algorithm is performed.
A comparison of results through MTrL and MTnL techniques consistently indicate a superior quality of approximations via the transversal linearization technique.
Note, however, that if the probability (Phi _{g,mathbb {P}}(B)) is small which is, e.g., the case if B is a "thin" set or has large distance from the center of the distribution (Phi _{g,mathbb {P}}) then relatively large sample sizes are needed for good approximations via simulation.
As a first step to handle these problems mathematically we introduce approximations via splines.
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