Rank structures preserved by the \(QR\)-algorithm: the singular case. (English) Zbl 1090.65044
In a previous paper the authors have shown that when the matrix \(A\) is nonsingular, the QR iterates share the same rank structure, which is defined through its blocks by Rank \(A_{k}(i_{k}:n,1:j_{k})\leq r_{k}\) where \(A_{k}=A-\lambda _{k}I.\) In this paper, it is shown that even when \(A\) is singular, they can still construct QR iterates that preserve the rank structure.
Reviewer: Amin Boumenir (Carrollton)
MSC:
| 65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
| 15A03 | Vector spaces, linear dependence, rank, lineability |
Keywords:
QR-algorithm; rank structure; Givens transformations; effectively eliminating QR-decompositions; sparse Givens patternsReferences:
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