When modified Gram-Schmidt generates a well-conditioned set of vectors

IMA Journal of Numerical Analysis

Volumn 22, Issue 4, 2002, Pages 521-528

  Giraud, L ^a   Langou, J ^a  

^a CERFACS   (France)

Author keywords

Floating point arithmetic; Gram Schmidt algorithm; Orthogonalization schemes

Indexed keywords

GRAM-SCHMIDT; GRAM-SCHMIDT ALGORITHMS; ILL-CONDITIONED; INITIAL MATRIXES; MACHINE PRECISION; MODIFIED GRAM-SCHMIDT ALGORITHM; NUMERICAL EXPERIMENTS; ORTHOGONALIZATION;

DIGITAL ARITHMETIC;

EID: 0036035449     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/22.4.521     Document Type: Article

References (6)

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2. BJÖRCK, Å. & PAIGE, C. C. (1992) Loss and recapture of orthogonality in the modified Gram-Schmidt Algorithm. SIAM J. Matrix Analysis and Applications, 13, 176-190.
3. GOLUB, G. H. & VAN LOAN, C. F. Matrix Computations. Baltimore, MA: Johns Hopkins University Press.
4. HIGHAM, N. J. (1994) The matrix sign decomposition and its relation to the polar decomposition. Linear Algebra and its Applications, 212/213, 3-20.
5. PARLETT, B. N. (1980) The Symmetric Eigenvalue Problem. Englewood Cliffs, NJ: Prentice-Hall.
6. WILKINSON, J. H. (1965) The Algebraic Eigenvalue Problem. Oxford: Oxford University Press.