Abstract
LetA andA+ΔA be Hermitian positive definite matrices. Suppose thatA=LDL H and (A+ΔA)=(L+ΔL)(D+ΔD)(L+ΔL)H are theLDL H decompositons ofA andA+ΔA, respectively. In this paper upper bounds on |ΔD| F and |ΔL| F are presented. Moreover, perturbation bounds are given for theLU decomposition of a complexn ×n matrix.
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References
A. Barrlund,Perturbation bounds on the polar decomposition, BIT 30: 1 (1990), 101–113.
G. H. Golub and C. F. Van Loan,Matrix Computations, 2nd Edition, Johns Hopkins University Press, Baltimore, Maryland 1989.
J.-G. Sun,Perturbation bounds for the Cholesky and QR Factorizations, BIT 31: 2 (1991), 341–352.
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Barrlund, A. Perturbation bounds for theLDL H andLU decompositions. BIT 31, 358–363 (1991). https://doi.org/10.1007/BF01931295
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DOI: https://doi.org/10.1007/BF01931295