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)

Variational characterizations of real eigenvalues of selfadjoint operators on a Hilbert space depending nonlinearly on an eigenparameter usually assume differentiable dependence of the operator onâ€¦ (More)

In 8] and 9] W. Mackens and the present author presented two generalizations of a method of Cybenko and Van Loan 4] for computing the smallest eigenvalue of a symmetric, positive deenite Toeplitzâ€¦ (More)

The Jacobiâ€“Davidson method is known to converge at least quadratically if the correction equation is solved exactly, and it is common experience that the fast convergence is maintained if theâ€¦ (More)

For solving the eigenvalue problem of a structural system having a large number of degrees of freedom the authors introduced in 6] the improved condensation method using the Rayleigh functional ofâ€¦ (More)

A nonlinear eigenvalue problem T (Î»)x = 0, the eigenvalues of which satisfy a minmax characterization shares many valuable properties of linear Hermitean eigenvalue problems. For instance, itsâ€¦ (More)