Pole swapping

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

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

Berkeley Lab Seminar

Abstract and slides for Berkeley Lab seminar.

A rational QZ method

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

ICIAM 2019

Abstract and slides for ICIAM 2019 presentation.

ETNA 25

Abstract and slides for ICIAM 2019 presentation.

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.

An implicit filter for rational Krylov using core transformations

This article proposes numerical algorithms to filter and restart the rational Krylov sequence method.

NASCA 2018

Abstract and slides for NASCA 2018 presentation.