Abstract
In this paper, the normative matrices and their doubleLR transformation with origin shifts are defined, and the essential relationship between the doubleLR transformation of a normative matrix and theQR transformation of the related symmetric tridiagonal matrix is proved. We obtain a stable doubleLR algorithm for doubleLR transformation of normative matrices and give the error analysis of our algorithm. The operation number of the stable doubleLR algorithm for normative matrices is only four sevenths of the rationalQR algorithm for real symmetric tridiagonal matrices.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Orega, J.M. and Kaiser, H.F., TheLL T andQR methods for symmetric tridiagonal matrices,Comput. J.,6 (1963/64), 99–101.
Reisch, C.H., A stable rationalQR algorithm for the computation of the eigenvalues of an Hermitian tridiagonal matrix,Math. of Comput.,25:115 (1971), 591–597.
Rutishauser, H, Solution of eigenvalue problem withLR transformation,Nat. Bur. Standards. Math. Ser.,49 (1958), 47–81.
Wilkinson, J.H., The Algebraic Eigenvalues Problem, Clarendon Press, Oxford, 1965.
Wilkinson, J.H., Global convergence of tridiagonalQR algorithm with origin shifts,linear Algebra and Its Applications 1 (1968), 409–420.
Jiang, E., The Computation of Symmetric Matrices, Shanghai Sci. and Technology Cop., 1984 (in Chinese).
Author information
Authors and Affiliations
Additional information
Supported by the Zhejiang Province Natural Science Foundation.
Rights and permissions
About this article
Cite this article
Daoqi, C. Stable doubleLR algorithm and its error analysis. Appl. Math. 9, 35–43 (1994). https://doi.org/10.1007/BF02662024
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02662024