First, we provide an exposition of a theorem due to Slodkowski regarding the largest "eigenvalue" of a convex function. In his work on the Dirichlet problem, Slodkowski introduces a generalized second-order derivative which for $C^2$ functions corresponds to the largest eigenvalue of the ...
We suggest to make a single partition of the feasible set in a concave variable only so that a convex approximation of the objective function upon every partition set has an acceptable error. Minimizing convex approximations on partition sets provides an approximate solution of the nonconvex ...
Eigenvalue decomposition plays a very vital role in easing the complexity of the matrix in the Linear Algebra field. The square matrix is broken down into
under proper conditions on the advection function $m$, we establish the asymptotic behavior of the principal eigenvalue as the advection coefficient $\alpha\to\infty$, and when $
Is the e^{ix} also an eigenfunction of the Hamiltonian? if so, what is the eigenvalue?Eigen function and eigen valueEigen value operations are those equations in which on operation on a function X by an operator say A , we get the function back only multiplied by a ...
Function arguments Iforder= TRUE or -1 (default) then the eigenvalues are arranged in descending order based on the absolute values of their real part. Iforder= FALSE or 0 then the eigenvalues are arranged in descending order of their real parts. Finally, iforder= +1 then the eigenv...
1. Several candidates for the function f in (1) where = 1 and = 2. on an interior point method [1]. The previous complication however is alleviated in case of graph Laplacians, where the smallest eigenvalue 1 (LG ) is always zero with the associated eigenvector of 1 composed...
Use of the spline function in Milne's method for eigenvalue problems of Sturm-Liouville-type linear equations is found to provide a high-speed method for calculating eigenvalues.doi:10.1016/0010-4655(90)90052-3Toshiaki YokotaTadashi YanoMasashi Otsuka...
The polyeig function uses the QZ factorization to find intermediate results in the computation of generalized eigenvalues. polyeig uses the intermediate results to determine if the eigenvalues are well-determined. See the descriptions of eig and qz for more information. The computed solutions might not...
Our purpose in this paper is to study the asymptotic behavior of the nonlinear eigenvalue problem, where {Omega} is a smooth bounded domain in R{sup 4}, {line_integral}(u) is an nonnegative smooth function with exponentially dominant nonlinearity and {lambda} > 0 is small. When {line_...