A Geometric Proof of Convergence for the QR Method |
Common terms and phrases
block of order BUUREMA Cauchy-Schwarz inequality columns complex number computation is performed compute a unitary denote F.L. BAUER follows functie G₁ G₂ h 1h h large h lim h h Xn+1 h+1 h+1 H₁₂ Hence Hessenberg form Hessenberg matrices Hessenberg matrix hh+1 infinite subset initial matrix invariant subspace inverse iteration iteration process Krylov sequences lemma lim p(r limit f limiting polynomial linear subspaces lower diagonal block mass-center method with shifts minimizing polynomial monic non-singular matrix normal matrix orthogonal complement p-dimensional subspace P₁ P₁o performed in real polynomial of degree PROOF OF CONVERGENCE QR algorithm QR method quence real arithmetic real numbers section 9 sequence of linear sequence of matrices SP2han strict inequality subspaces converges tary matrix tend to zero unitary matrix vectors x+z W₂ wiskunde X₁₂ X₂ zijn