For the nonlinear eigenvalue problem T (Î»)x = 0 we propose an iterative projection method for computing a few eigenvalues close to a given parameter. The current search space is expanded by aâ€¦ (More)

where T (Î») âˆˆ R is a family of symmetric matrices depending on a parameter Î» âˆˆ J , and J âŠ‚ R is an open interval which may be unbounded. As in the linear case T (Î») = Î»I âˆ’A a parameter Î» is called anâ€¦ (More)

We discuss the state of the art in numerical solution methods for large scale polynomial or rational eigenvalue problems. We present the currently available solution methods such as theâ€¦ (More)

The total least squares (TLS) method is a successful approach for linear problems if both the system matrix and the right hand side are contaminated by some noise. For ill-posed TLS problems Renautâ€¦ (More)

This article discusses a projection method for nonlinear eigenvalue problems. The subspace of approximants is constructed by a Jacobiâ€“Davidson type approach, and the arising eigenproblems of smallâ€¦ (More)

For the nonlinear eigenvalue problem T (Î»)x = 0 we consider a Jacobiâ€“Davidson type iterative projection method. The resulting projected nonlinear eigenvalue problems are solved by inverse iteration.â€¦ (More)

In this paper we consider sparse, symmetric eigenproblems which are rational perturbations of small rank of linear eigenproblems. Problems of this type arise in structural dynamics and in vibrationsâ€¦ (More)

Abstract. The Automated Multi-Level Substructuring (AMLS) method has been developed to reduce the computational demands of frequency response analysis and has recently been proposed as an alternativeâ€¦ (More)

In and W Mackens and the present author presented two generaliza tions of a method of Cybenko and Van Loan for computing the smallest eigenvalue of a symmetric positive de nite Toeplitz matrix Takingâ€¦ (More)