This research focuses on nding a large number of eigenvalues and eigenvectors of a sparse symmetric or Hermitian matrix, for example, nding 1000 eigenpairs of a 100,000 100,000 matrix. These eigenvalue problems are challenging because the matrix size is too large for traditional QR based algorithms and the number of desired eigenpairs is too large for most common sparse eigenvalue algorithms. I...

Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...

The inherent uncertainties in geometry, material properties, etc. of engineering structures can be represented by stochastic models, where the parameters are described by probabilistic laws. Results from any analysis based on stochastic models inherit probabilistic information as well, which can be used e.g. for reliability analysis. Particularly in linear dynamics of structures the calculation...