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Linear convergence in the shifted ๐‘„๐‘… algorithm

Linear convergence in the shifted ๐‘„๐‘… algorithm

Global and asymptotic convergence properties for the QR algorithm with Francis double shift are established for certain orthogonal similarity classes of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="4 times 4"> <mml:semantics> <mml:mrow> <mml:mn>4</mml:mn> <mml:mo>ร—<!-- ร— --></mml:mo> <mml:mn>4</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">4 \times 4</mml:annotation> </mml:semantics> </mml:math> </inline-formula> real matrices. It is shown that in โ€ฆ