The accuracy of Arnoldi's method is tested by comparing the dominant eigenvalues with the rate of convergence of the iterative method.
The homogeneous case is also studied and its relation to the sandwich beam is set forth by comparing the corresponding eigenvalues.
Random Matrix Theory estimates the number of significant components of a data covariance matrix by comparing the statistics of the observed eigenvalues obtained from PCA with those obtained from a random matrix.
Equality between the elements of the two matrices is estimated by comparing the extent of departure between their respective ranked eigenvalues after eigen-decomposition of each matrix [ 25].
Motivated by [4], we compare the eigenvalues of the eigenvalue problem (1.1) with the coupled boundary condition (1.2) as varies and obtain relationships between the eigenvalues in the present paper.
In this paper, we will apply some results obtained by Shi and Chen [2] to prove the existence of eigenvalues of (1.1) and (1.2) to calculate the number of these eigenvalues, and to apply some oscillation results obtained by Agarwal et al. [9] to compare the eigenvalues as varies.
Instead, we will make use of some oscillation results that are extended from the results obtained by Agarwal et al. [4] to prove the existence of eigenvalues of (1.1) with (1.2) and compare the eigenvalues as varies.
Moreover, in Supplementary Material 9 we also compare the eigenvalue curves using different K values as input.
The estimate of the population eigenvalues is updated by comparing these sample eigenvalues with the measured eigenvalues.
