Pole swapping

The RQR algorithm

This article adapts pole swapping algorithms to the standard eigenvalue problem.

A multishift, multipole rational QZ method with aggressive early deflation

An extension of the rational QZ method for the solution of the real generalized eigenvalue problems with aggressive early deflation.

On pole-swapping algorithms for the eigenvalue problem

This article studies a convergence theory applicable to all pole-swapping methods. It proposes a backward stable algorithm to compute a pole swap in finite precision.

Pole swapping methods for the eigenvalue problem - Rational QR algorithms

Presentation for Public PhD Defence at KU Leuven.

Pole swapping methods for the eigenvalue problem: Rational QR algorithms

PhD thesis on pole swapping algorithms for standard and generalized eigenvalue problems.

Pole swapping methods for the eigenvalue problem - Rational QR algorithms

Seminar presentation on pole swapping algorithms presented at Lawrence Berkeley National Laboratory.

A rational QZ method

This article proposes a rational QZ method for the solution of the generalized eigenvalue problem.

Pole swapping methods for the eigenvalue problem - Rational QR algorithms

Talk on the multishift, multipole rational QZ algorithm presented at ICIAM 2019 Conference in Valencia, Spain.

Approximate inverse-free rational Krylov methods and the link with FOM and GMRES

Talk on approximate rational Krylov methods presented at the ETNA25 conference in Santa Margherita di Pula, Italy.

Swapping 2 × 2 blocks in the Schur and generalized Schur form

This article proposes numerical algorithms to reorder 2 x 2 blocks in a real Schur form and a generalized real Schur form.