On the Error in the Product QR Decomposition | Zendy

Erik S. Van Vleck | Zendy

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On the Error in the Product QR Decomposition

Author(s) -

Erik S. Van Vleck

Publication year - 2010

Publication title -

siam journal on matrix analysis and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.268

H-Index - 101

eISSN - 1095-7162

pISSN - 0895-4798

DOI - 10.1137/090761562

Subject(s) - mathematics , invertible matrix , qr decomposition , factorization , eigenvalues and eigenvectors , triangular matrix , degree (music) , product (mathematics) , matrix decomposition , pure mathematics , algorithm , geometry , acoustics , physics , quantum mechanics

We develop both a normwise and a componentwise error analysis for the QR factorization of long products of invertible matrices. We obtain global error bounds for both the orthogonal and upper triangular factors that depend on uniform bounds on the size of the local error, the local degree of nonnormality, and integral separation, a natural condition related to gaps between eigenvalues but for products of matrices. We illustrate our analytical results with numerical results that show the dependence on the degree of nonnormality and the strength of integral separation.

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