Sentence examples for bound for the best from inspiring English sources

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Ideal separation: This method performs as an upper bound for the best separation that can be achieved with the used time-frequency representation.

The following theorem then gives an upper bound for the best approximation error of Theorem 1: Assume the exact solution of (3 -(4) is such that (mathbf {A} in mathbf {H}(mathbf {curl},Omega ) cap H^{s}({Omega_{1}, Omega_{2}})^{3}), (nablatimes mathbf {A} in H^{s}({Omega_{1}, Omega_{2}})^{3}) with integer (1 leq s leq k).

We find that the use of the lower Hashin Shtrikman bound for the LCC gives the best predictions by comparison with the unit cell calculations for both the macroscopic stress-strain response as well as for the average strains in each of the phases.

The best error bound for the system P z ≤ Q x + q is denoted α ′.

The best iteration bound for the LO problem, which was given by Bai et al. [6], is O ( n log n log n ϵ ).

We give the best lower bound for the weighted Jensen's discrete inequality with ordered variables applied to a convex function, in the case when the lower bound depends on, weights, and two given variables.

D is said to be a small k-dominating set if it has at most [n/k+1] nodes, which is the best lower bound for the size of D in general.

Then, the relative gap for this solution measures the distance between z B and the available best bound for the optimal objective function value (z L ) using the ratio | z B − z L | z L. LP-based branch-and-bound algorithms are used for solving MIPs in GAMS [31]; thus, z L is the LP relaxation solution of the MIP problem under consideration.

This improves the best known lower bound for the Shannon capacity of the graph C7 which is the zero-error capacity of the corresponding noisy channel.

Since Ψ 0 1 / 2 = O ( r ), if we take p = O ( log r ) and q = 1, then we can get the best known upper bound for the total number of inner iterations in the outer iteration is O ( r log r ).