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Using the estimate (3.37), we obtain the l2 upper bound for the approximation error induced by the simple shrinkage procedure4.
Instead of (15), we seek a bound for the approximation error that provides some indication on the trade-off between the number of independent filters, M, and the number of particles per filter, N.
After the spatial discretization, we obtain the l2 upper bound for the approximation error introduced by a simple shrinkage procedure, where we take the generator vectors from the DCT over-complete dictionary.
We optimize with respect to (αK+1,..., αK+m) and get new, suboptimal, approximate 5. We continue with adding vectors as previously explained, until l2 upper bound for the approximation error becomes lower than ε.
This inequality gives an upper bound for the approximation of the integral average 1 b − a ∫ a b f ( t ) d t by the value f at a point x ∈ ( a, b ).
Iyengar proved a useful inequality which gives an upper bound for the approximation of the integral average by the mean of the values of mapping at end points of the interval that is given below (see [7] or [11, p.471]).
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The upper l2 bound for the patch approximation error for all experiments was set to ε = 0.05.
Moreover, when the additional hypothesis | E [ e i t ξ 1 ] | = o ( | t | − p ), for | t | → + ∞, is in force with some p > 0 (to be compared with (14) in [5]), it is possible to deduce a bound for the normal approximation w.r.t. the total variation distance, by following the argument developed in [18].
Input ϵ is a bound for the total approximation error caused by the solutions of the ODEs in line 13.
The CFVP gives us the explicit upper bound for the L2 norm of the approximation error.
In this paper we present a new approximation for computing lower bound for the fixed charge transportation problem (FCTP).
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