The DQR algorithm, basic theory, convergence, and conditional stability
The work is dedicated to the general eigenvalue problem and discusses the DQR method as an alternative to the standard QR algorithm. The given dense matrix is reduced to general tridiagonal form (instead of Hessenberg form). For the iterative part D-orthogonal similarity transformations are used, which preserve the tridiagonal structure and thus allow computation of all eigenvalues with \(O(n^2)\) flop. Since the DQR method can be unstable the author proposes a hybrid algorithm, which switches to standard QR if application of DQR fails. The article contains theoretical investigations of convergence and stability behavior of the DQR method as well as exhaustive discussions of numerical examples.
scientific article; zbMATH DE number 1037313