Broyden's Method for Nonlinear Eigenproblems

A Jacobi-Davidson Method for Nonlinear Eigenproblems

For the nonlinear eigenvalue problem T (λ)x = 0 we consider a Jacobi–Davidson type iterative projection method. The resulting projected nonlinear eigenvalue problems are solved by inverse iteration. The method is applied to a rational eigenvalue problem governing damped vibrations of a structure.

Rational Krylov for Nonlinear Eigenproblems, an Iterative Projection Method

In recent papers Ruhe [10], [12] suggested a rational Krylov method for nonlinear eigenproblems knitting together a secant method for linearizing the nonlinear problem and the Krylov method for the linearized problem. In this note we point out that the method can be understood as an iterative projection method. Similar to the Arnoldi method presented in [13], [14] the search space is expanded b...

Multilevel Method for Mixed Eigenproblems

Rational Krylov for Large Nonlinear Eigenproblems

Rational Krylov is an extension of the Lanczos or Arnoldi eigenvalue algorithm where several shifts (matrix factorizations) are used in one run. It corresponds to multipoint moment matching in model reduction. A variant applicable to nonlinear eigenproblems is described.

Linear and Nonlinear Eigenproblems for PDEs

The workshop discussed the numerical solution of linear and nonlinear eigenvalue problems for partial differential equations. It included the theoretical analysis the development of new (adaptive) methods, the iterative solution of the algebraic problems as well as the application in many areas of science and engineering. Mathematics Subject Classification (2000): 65N25, 65F15, 15A18. Introduct...