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In this paper, we propose a novel online RPCA algorithm by adopting a recently proposed truncated nuclear norm as a tighter approximation of low rank constraint.
As it is shown in Fig. 10a, introducing control leads to a tighter approximation of the simulation results from the numerical ones, compared to the absence of control.
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1) The increase of objective function costs and solution times with respect to tighter approximations for all instances examined.
The overall objective function (sum of (C_{mathrm{e}}), (C_{mathrm{c}}), and (C_{mathrm{s}})) is always higher for tighter approximations due to reduced feasible sets.
The average power is in general higher for tighter approximations and moreover higher for higher non-electric gas loads, thus especially during the evening.
Thus, the solution, ({ {{hat {mathbf {Q}}}_{mathbf {v}}},{{hat {mathbf {Q}}}_{J}} }), is indeed a tight approximation of (32).
We need to calculate the TGVP for a relatively large number of time-slots K to obtain a tight approximation.
Furthermore, analyzing the high signal-to-noise ratio (SNR) regime, we derive an asymptotically tight approximation for SEP.
This finding helps us to derive the asymptotically tight approximation of SEP for both AF and HDAF relay protocols.
Since we have assumed uncorrelated time-slots to obtain our TGVP approximation, we will therefore have a less tight approximation for short time-slots.
Moreover, using the asymptotic approximation of in (A.10), a tight approximation of in the high can be obtained as follows: (20).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com