Because the eigenvalue equation
for a given frequency, [omega], is quadratic in k, it can be transformed to a linear eigenvalue problem of the form:
Then, the eigenvalue equation can be simplified as follows:
The eigenvalue equation has the similar solution to that of the translation mode under the condition the rotor speed of the MSFW is zero.
By applying the variational operation to recast Equation (2), the spatial basis can be obtained from the following eigenvalue equation
Using (22) and (52), the Energy eigenvalue equation
for the potential under the consideration following as
According to Proposition 2, the problem of solving the constrained optimization function is transformed to the problem of solving eigenvalue equation
shown in (19).
The calculations involved in trying to directly solve an eigenvalue equation
for an actual system of say, one million equations, would be formidable.
The solutions of the eigenvalue equation Cx = x[lambda] imply the given quadratic equation and its solutions.
as well) obey all the same eigenvalue equation (cf.
Objective: Models and Algorithms for Graph centrality grounded on Nonlinear Eigenvalues TechniquesThe main objective of the project is to use nonlinear eigenvalue equations
to model the importance of components in complex, large-scale and time-varying networks.
The eigenvalue equations
are then reduced to a finite linear system: