Sentence examples for by differentiating the eigenvalue from inspiring English sources

Explicit expressions of the first and second order derivatives of natural frequencies and eigenvectors with respect to the configuration parameters are derived by differentiating the eigenvalue equation.

In the case of three distinct eigenvalues, the derivatives of these tensor functions are constructed by solving a tensor equation, which is acquired by differentiating the commutative condition.

Our conclusion is followed by differentiating the term g ○ ϕ.   □.

By differentiating the above equality, we get (2.8).

The desired coefficients are then obtained by differentiating the relevant polynomials.

The linear small signal model is derived by differentiating the averaged model around its equilibrium point.

The ion energies can be computed by differentiating the data.

It is further pointed out that even though the sensitivity analysis formula of frequencies has been corrected, the first derivatives of frequencies with respect to design variables cannot be achieved by direct differentiating the equations of eigenvalues and eigenvectors because the first derivatives of vibration modes with respect to design variables are still unknown.

Accurate reaction field forces are obtained by directly differentiating the electrostatic potential.

It is shown that F(A) can be obtained by differentiating a scalar function of the eigenvalues of A. Using this method, closed-form, singularity-free expressions of arbitrary tensor functions and their first derivatives are deduced in two- and three-dimensional cases.

By differentiating ourselves from the competition.