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Optimization errors are bounded in terms of the volume-dispersion.
Then (|G/V|) is bounded in terms of (k) and (alpha ) alone.
The error is bounded in terms of the infinity norms of the noise and a derivative of the signal.
Since and, we conclude that both and are bounded, and consequently and are also bounded in terms of (3.24).
In [15], the sum rate for a system with training-based CSIT is lower bounded in terms of the sum rate of a related system with perfect CSIT.
Under assumptions (HA) to (HD), the solution u to problem (P1) in [0,1] × [0,T], given by Theorem 1, is bounded in terms of the initial and boundary data h, f and g.
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Now we give the error bounds in terms of the residual function (Vert e x,rho Vert ).
Validation provides a slightly better performance than the subset ambiguity bounding in terms of the integer fixing failure rates and the computational efficiency.
In Section 4, we introduce the D-gap function and derive global error bounds in terms of the D-gap function for the solution of SVMQVIP (1.1).
The second ingredient is a lower bound for the coercivity constant α N , 0 < α LB N ≤ α N , ∀ μ ∈ D. We can now define our error bounds in terms of these two ingredients; in fact, it can readily be proven [22, 31] that for all μ ∈ D and all N (54).
A useful characterization of a statistically bounded sequence in terms of its bounded subsequence has been given by Tripathy [31] as follows.
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