This system, together with inequalities which guarantee positive definiteness of the matrix M, results in a one parameter family of inner products which give exact gradients for linear functions.
We provide a simple modification which brings some desirable features by omitting the second term from the Hessian matrix and diagonal loading to guarantee positive definiteness H ≈ 2 R X F H F X H + α I. (27).
In all other instances, the use of a regularized estimator is absolutely vital (e.g., the Stein-type shrinkage estimator of [ 20]) in order to improve efficiency and to guarantee positive definiteness.
We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities.
This is sufficient to guarantee the positive definiteness of (B_{k+1}) as long as (B_{k}) is positive definite.
In the programmed procedure, we employ the stochastic selecting algorithm to exclude rigid-body motions, the restricted step algorithm to guarantee the positive definiteness of the structural stiffness matrix, and the line search algorithm to minimize the total potential energy.
end{aligned} (17) Lately, to guarantee the positive definiteness of σ a.e. in Ω̄ in the sense of (H2), we have to impose, inter alia, that (sigma_{xx}sigma_{yy}- sigma_{xy})^{2}> 0) a.e. in Ω̄.
It should be pointed out that the Hessian matrix U ‡ varies with the synthesized sequence at the optimization process, and the parameter λ i should change with the smallest singular value of U ‡ (s i ) to guarantee the positive definiteness of the Hessian matrix.
The constitutive equation is solved using a scheme that guarantees the positive definiteness of the configuration tensor, while the convection term in the constitutive equation is discretized using a third-order upwinding scheme.
Several approaches generalize the constant correlation to a time-varying and stochastic concept, like Dynamic Conditional Correlation model in [6], Local correlation models see e.g. [7] and the Wishart autoregressive process proposed by Gourieroux [8] that guarantees the positive definiteness of the variance-covariance matrix.
In the definition of the Riemann theta function, the positive definiteness of τ guarantees (2.7) converges absolutely for all values of ξ.
