The phrase "approximation of the left" is correct and usable in written English.
It can be used in contexts where you are discussing a mathematical or conceptual approximation related to the left side of an equation, graph, or other relevant subject.
Example: "In our calculations, we found that the approximation of the left yields a value close to the expected result."
Alternatives: "estimate of the left" or "calculation of the left".
In the case of time-series data, we proceed by applying the finite difference approximation to the left hand side of Equation (1), isolating the unknown parameters β on the right hand side, and dividing both sides by.
Furthermore, the so-called proper orthogonal decomposition approximation uses the left dominant subspace of a matrix A where a column consists of a time instance of the solution of an evolution equation, e.g., the flow field from a fluid dynamics simulation.
Theorem 1 implies that selecting a transform that features the best energy compaction with the smallest number of transform coefficients secures the best approximation of (left{ {A^{N} } right}) for a given subset (left{ {A^{K} } right}) of its samples.
This is true due to the approximation of left| {Delta varvec{z}_{1} (t)} right| approx e^{{M_{text{MCLE}} t}} left| {Delta varvec{z}_{1}^{0} } right| (11) Open image in new window Fig. 3 Nearby trajectories in the state space.
The corresponding best approximation problems for the left and right inverse eigenvalue problem are also solved.
A better approximation of left tail regions is desirable, as it has the potential to contribute larger scores.
In Figure 6, we give the comparison among the numerical solution of system (1.3) (left), the weakly nonlinear first order approximation of the solution (medium) and the weakly nonlinear fifth order approximation of the solution (right) under subcritical case.
The result of their work is twofold: on the one hand, they achieve an approximation order (0(h^5)) for the left method, on the other hand, they achieve another approximation of the order of (0(h^6)) for the right method.
PEV for genetic evaluations are routinely produced, either by computationally intensive direct inversion of the left hand side of the mixed model equations or, where this is not possible, by approximations [ 3– 7] or selection index theory [ 8, 9].
