Rational QZ steps with perfect shifts
Rational QZ steps with perfect shifts
Abstract In this paper we analyze the stability of the problem of performing a rational QZ step with a shift that is an eigenvalue of a given regular pencil $$H-\lambda K$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>-</mml:mo> <mml:mi>λ</mml:mi> <mml:mi>K</mml:mi> </mml:mrow> </mml:math> in unreduced Hessenberg–Hessenberg form. In exact arithmetic, the backward rational …