The computation of compact and meaningful representations of high dimensional sensor data has recently been addressed through the development of Nonlinear Dimensional Reduction (NLDR) algorithms. The numerical implementation of spectral NLDR techniques typically leads to a symmetric eigenvalue problem that is solved by traditional batch eigensolution algorithms. The application of such algorith...

In this study, the symplectic method is applied to a two-dimensional annular-sector viscoelastic domain under the polar coordinate system. By applying variable separation approach, all fundamental solutions are derived in analytical form. Furthermore, using the method of variable substitution, lateral conditions are transformed into finding a particular solution for the governing equations, and...

The implicitly restarted Arnoldi method implicitly applies a polynomial lter to the Arnoldi vectors by use of orthogonal transformations. In this paper, an implicit ltering by rational functions is proposed for the rational Krylov method. This ltering is performed in an eecient way. Two applications are considered. The rst one is the ltering of unwanted eigenvalues using exact shifts. This appr...

Computation of eigenvalues and eigenvectors of a dense symmetric matrix is one of the most important problems in numerical linear algebra. In applications such as molecular orbital methods and first-principles molecular dynamics, eigensolution of matrices of order more than 10,000 is now needed. One of the approaches to solve such a large problem in practical time is to use symmetric multi-proc...

The Lanczos eigensolution takes the dominant amount of time in most normal modes and modal frequency response analyses. This paper introduces a way to reduce the elapsed time of large eigenvalue jobs by using a newly developed parallel option within the Lanczos algorithm. We will compare the performance of the frequency domain decomposition based distributed memory parallel method introduced in...

Abstract. We construct the asymptotic approximation to the first eigenvalue and corresponding eigensolution of Laplace’s operator inside a domain containing a cloud of small rigid inclusions. The separation of the small inclusions is characterized by a small parameter which is much larger when compared with the nominal size of inclusions. Remainder estimates for the approximations to the first ...