A deeation procedure is introduced that is designed to improve the convergence of an implicitly restarted Arnoldi iteration for computing a few eigenvalues of a large matrix. As the iteration progresses the Ritz value approximations of the eigenvalues of A converge at diierent rates. A numerically stable scheme is introduced that implicitly deeates the converged approximations from the iteratio...

The dual Craig-Bampton method can suffer from the fact that the reduced system has negative eigenvalues. Those negative eigenvalues are related to modes with weak interface compatibility and can be present in the lower frequency range when the reduction space is too poor. In this paper we investigate is so-called Modal Truncation vectors related to the interface forces can be used in the reduct...

We present and describe two new speaker adaptation methods which apply principal component analysis to maximum likelihood linear regression (MLLR). If we apply MLLR after transforming the baseline mean vectors by their eigenvectors, the contributions of these eigenvalues to the variance of the estimates for the MLLR matrix are inversely proportional to their corresponding eigenvalues. In the fi...

Transfer matrices are used widely for the dynamic analysis of engineering structures, increasingly so for static analysis, and are particularly useful in the treatment of repetitive structures for which, in general, the behaviour of a complete structure can be determined through the analysis of a single repeating cell, together with boundary conditions if the structure is not of infinite extent...

in this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

An implicitly restarted symplectic Lanczos method for the symplectic eigenvalue problem is presented. The Lanczos vectors are constructed to form a symplectic basis. The inherent numerical diiculties of the symplectic Lanczos method are addressed by inexpensive implicit restarts. The method is used to compute some eigenvalues and eigenvectors of large and sparse symplectic matrices.

The analysis of a number of physical phenomena requires the solution of an eigenproblem. It is therefore natural that with the increased use of computational methods operating on discrete representations of physical problems the development of efficient algorithms for the calculation of eigenvalues and eigenvectors has attracted much attention [l]-[8]. In particular, the use of finite element a...

We prove that the maximum of the sample importance weights in a high-dimensional Gaussian particle filter converges to unity unless the ensemble size grows exponentially in the system dimension. Our work is motivated by and parallels the derivations of Bengtsson, Bickel and Li (2007); however, we weaken their assumptions on the eigenvalues of the covariance matrix of the prior distribution and ...

We study the Lanczos method for computing extreme eigenvalues of a symmetric or Hermitian matrix. It is not guaranteed that the extreme Ritz values are close to the extreme eigenvalues—even when the norms of the corresponding residual vectors are small. Assuming that the starting vector has been chosen randomly, we compute probabilistic bounds for the extreme eigenvalues from data available dur...

We determine the joint distribution of the lengths of, and angles between, the N shortest lattice vectors in a random n-dimensional lattice as n → ∞. Moreover we interpret the result in terms of eigenvalues and eigenfunctions of the Laplacian on flat tori. Finally we discuss the limit distribution of any finite number of successive minima of a random n-dimensional lattice as n → ∞.