Sentence examples for by replacing the quadratic from inspiring English sources
In this paper, we propose the cubic body wave equation as an extension to Barrett's formulation by replacing the quadratic amplitude expression by a cubic spline polynomial.
The ridge regression [39] problem in Equation 2 can be transformed into the SVR optimization problem by replacing the quadratic loss with the ε-insensitive linear loss, l ε (f(x i ) − y i ) = max{0,f(x i ) − y i } which is shown in Figure 1B: min w, b ∥ w ∥ 2 + C ∑ i = 1 m ξ + ξ ∗ subject to: f ( x i ) - y i ≤ ε + ξ y i - f ( x i ) ≤ ε + ξ ∗ ξ, ξ ∗ ≥ 0 (3).
This is achieved by replacing the purely quadratic cost function employed within the MPC optimization by a mixed linear-quadratic cost function.
We next show that replacing the quadratic objective and constraint functions with their convex envelopes is dominated by an alternative methodology based on convexifying the range of the bilinear terms on the feasible region.
Firstly, by replacing the constant amplitude by a quadratic amplitude wave and secondly, by provisioning that α can act as both an amplitude growth and dampening factor.
By replacing a quadratic term ∥ y − x ∗ ∥ 2 in the subproblem (1.1) by the Bregman distance function, Nguyen et al. in [15] proposed the interior proximal extragradient method for solving EP ( f, C ), where f is pseudomonotone and C only is a polyhedron convex set.
The method is based on the special interior proximal function which replaces the usual quadratic function.
The method is based on a special interior proximal function which replaces the usual quadratic function.
This corresponds to replacing
In particular, because the steady-state solution to Eq. (17), for the master equation 5 involves only quadratic moments, the relation can be closed by replacing I + n J by ⟨ I + n J ⟩ and P + n0 by ⟨ P + n0⟩ in Eq. 5 and then evaluating the relation (17) at d⟨ n⟩/ dt = 0.
The first author treating the stability of the quadratic equation was Skof [27] by proving that if f is a mapping from a normed space X into a Banach space Y satisfying ||f(x + y) + f(x -y)- 2f(x) - 2f y)|| ≤ ε for some ε > 0, then there is a unique quadratic mapping g: X → Y such that f ( x ) - g ( x ) ≤ ε 2. Cholewa [28] extended the Skof's theorem by replacing X by an abelian group G.
