Rational Krylov for Nonlinear Eigenproblems, an Iterative Projection Method

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...

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.

Iterative Dual Rational Krylov and Iterative SVD-Dual Rational Krylov Model Reduction for Switched Linear Systems

In this paper, we propose two models reduction algorithms for approximation of large-scale linear switched systems. We present at first the iterative dual rational krylov approach, that construct a union of krylov subspaces. The iterative dual rational Krylov is low in cost, numerical efficient but the stability of reduced system is not always guaranteed. In the second part we present, the iter...

Krylov Projection Methods for Rational Interpolation

Convergence of the Iterative Rational Krylov Algorithm

The iterative rational Krylov algorithm (IRKA) of Gugercin et al. (2008) [8] is an interpolatory model reduction approach to the optimal H2 approximation problem. Even though the method has been illustrated to show rapid convergence in various examples, a proof of convergence has not been provided yet. In this note, we show that in the case of state-space-symmetric systems, IRKA is a locally co...