eigenvalue problem


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eigenvalue problem

[′ī·gən‚val·yü ‚präb·ləm]
(mathematics)
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The problem (3.2) is associated with the matrix eigenvalue problem
We choose a block size of 10 and use a Cholesky decomposition of the right-hand side of the eigenvalue problem as local preconditioner.
Then, similarly, the eigenvalue problem linearized at ([U.sub.[gamma]], 0) is
It is the purpose of this paper to show the existence of the principal eigenvalues and determine the sign of the corresponding eigenfunctions for linear periodic eigenvalue problem
Saad, "Asymptotic iteration method for eigenvalue problems," Journal of Physics A: Mathematical and General, vol.
In order to determine the solution of the eigenvalue problem ((16)-(17)) we use the following Mittag-Leffler function:
Next, in order to prove the existence of at least two positive solutions, we may use reduction to absurdity and suppose that (3) has a unique coexistence state ([mathematical expression not reproducible]); it follows from local bifurcation theory that solutions must be positive solutions bifurcated from ([mathematical expression not reproducible]) is nondegenerate and the corresponding linearized eigenvalue problem has a unique eigenvalue [mathematical expression not reproducible] with multiplicity one.
then the fractional Sturm-Liouville eigenvalue problem (3) can be written as
Substitution of the separable solution u = [chi][e.sup.[lambda]t] into (11) gives the gyroscopic state eigenvalue problem:
Since we, in this paper, deal with the improving of the algorithm to determine whether a quadratic eigenvalue problem is definite or not, let us briefly summarize what has been done so far in the literature up to this point.
where [[PHI].sub.0] are the eigenvectors of the original (baseline) design, and the following eigenvalue problem is solved