Sentence examples similar to ensure definiteness from inspiring English sources
To ensure positive definiteness of B, we must have x T B x = x T x − x T A Σ b A T x > 0 (26).
If we cannot find suitable constants g, h, β, and ξ to ensure positive definiteness, or such constants do not exist, Theorem 1 is not applicable.
If we cannot find suitable matrices (G_{1}), (G_{2}), H, and constants (beta>0), (zeta>0) to ensure positive definiteness, or such matrices and constants do not exist, then Theorem 5 is not applicable.
Although we can threshold the eigenvalues of the Hessian matrix to ensure positive definiteness, this method might generate useless coefficients.
Official correlations differ from correlation estimates due to post-processing to ensure positive definiteness and averaged about 0.90 but were lower for New Zealand than for the other countries.
One way to ensure positive-definiteness of V ρ i is to introduce a ridge parameter in its formulation [ 62].
We present two matrix decompositions that enable us to construct the conformational tensor in a manner that ensures positive definiteness.
In order to ensure the positive definiteness of (B_{k}), in Step 4 of the main algorithm: if (y_{k}^{T}s_{k}>0), update (B_{k}) by (1.11), otherwise let (B_{k+1}=B_{k}).
The condition (frac {beta }{alpha }<frac {1}{|A|^{2}}) <span class="lh lhl">ensures the positive definiteness of P. The technique of introducing the term (u−u k )P u−u k ) was used earlier in [25].
(iv) Assigning a Hurwitz closed-loop Jacobian and ensuring positive semi-definiteness of the closed-loop dissipation matrix, the tedious definiteness check of the energy is omitted.
