메뉴 건너뛰기




Volumn 11, Issue 7, 2004, Pages 675-692

Computing projections via Householder transformations and Gram-Schmidt orthogonalizations

Author keywords

Accurate computation of small projections; Gram Schmidt orthogonalizations; Householder transformations; Iterative refinement

Indexed keywords


EID: 10044270004     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.384     Document Type: Article
Times cited : (2)

References (30)
  • 1
    • 0036457812 scopus 로고    scopus 로고
    • Loss and retention of accuracy in affine scaling methods
    • Dax A. Loss and retention of accuracy in affine scaling methods. Optimization Methods and Software 2001; 15:121-151.
    • (2001) Optimization Methods and Software , vol.15 , pp. 121-151
    • Dax, A.1
  • 9
    • 0033233451 scopus 로고    scopus 로고
    • Row-wise backward stable elimination methods for the equality constrained least squares problem
    • Cox AJ, Higham NJ. Row-wise backward stable elimination methods for the equality constrained least squares problem. SIAM Journal on Matrix Analysis and Applications 1999; 21:313-326.
    • (1999) SIAM Journal on Matrix Analysis and Applications , vol.21 , pp. 313-326
    • Cox, A.J.1    Higham, N.J.2
  • 10
    • 0346435065 scopus 로고
    • On modified Gram-Schmidt for weighted and constrained linear least squares problems
    • Gulliksson M. On modified Gram-Schmidt for weighted and constrained linear least squares problems. BIT 1995; 35:453-468.
    • (1995) BIT , vol.35 , pp. 453-468
    • Gulliksson, M.1
  • 11
    • 0012031765 scopus 로고    scopus 로고
    • Implicit scaling of linear least squares problems
    • Reid JK. Implicit scaling of linear least squares problems. BIT 2000; 40:146-157.
    • (2000) BIT , vol.40 , pp. 146-157
    • Reid, J.K.1
  • 12
    • 0001713407 scopus 로고    scopus 로고
    • On the weighting method for least squares problems with linear equality constraints
    • Stewart GW. On the weighting method for least squares problems with linear equality constraints. BIT 1997; 37:961-967.
    • (1997) BIT , vol.37 , pp. 961-967
    • Stewart, G.W.1
  • 13
    • 0022146092 scopus 로고
    • On the method of weighting for equality-constrained least-squares problems
    • Van Loan C. On the method of weighting for equality-constrained least-squares problems. SIAM Journal on Numerical Analysis 1985; 22:851-864.
    • (1985) SIAM Journal on Numerical Analysis , vol.22 , pp. 851-864
    • Van Loan, C.1
  • 14
    • 0001241476 scopus 로고
    • On applying Householder transformations to linear least squares problems
    • Theoretical Physics Division, Harwell Laboratory
    • Powell MJD, Reid JK. On applying Householder transformations to linear least squares problems. Report TP 322, Theoretical Physics Division, Harwell Laboratory, 1968.
    • (1968) Report TP , vol.322
    • Powell, M.J.D.1    Reid, J.K.2
  • 15
    • 0001241476 scopus 로고
    • On applying Householder transformations to linear least squares problems
    • Morrell AJH (ed.). North-Holland: Amsterdam
    • Powell MJD, Reid JK. On applying Householder transformations to linear least squares problems. In Information Procession, Morrell AJH (ed.). vol. 68. North-Holland: Amsterdam, 1969; 122-126.
    • (1969) Information Procession , vol.68 , pp. 122-126
    • Powell, M.J.D.1    Reid, J.K.2
  • 16
    • 0034379461 scopus 로고    scopus 로고
    • A modified Gram-Schmidt algorithm with iterative orthogonalization and column pivoting
    • Dax A. A modified Gram-Schmidt algorithm with iterative orthogonalization and column pivoting. Linear Algebra and its Applications 2000; 310:25-42.
    • (2000) Linear Algebra and Its Applications , vol.310 , pp. 25-42
    • Dax, A.1
  • 17
    • 84966217951 scopus 로고
    • Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization
    • Daniel JW, Gragg WB, Kaufman L, Stewart GW. Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization. Mathematics of Computation 1976; 30:772-795.
    • (1976) Mathematics of Computation , vol.30 , pp. 772-795
    • Daniel, J.W.1    Gragg, W.B.2    Kaufman, L.3    Stewart, G.W.4
  • 18
    • 0000319891 scopus 로고
    • Numerical aspects of Gram-Schmidt orthogonalization of vectors
    • Ruhe A. Numerical aspects of Gram-Schmidt orthogonalization of vectors. Linear Algebra and its Applications 1983; 52/53:591-601.
    • (1983) Linear Algebra and Its Applications , vol.52-53 , pp. 591-601
    • Ruhe, A.1
  • 19
    • 0024776757 scopus 로고
    • Iterative algorithms for Gram-Schmidt orthogonalization
    • Hoffmann W. Iterative algorithms for Gram-Schmidt orthogonalization. Computing 1989; 41:335-348.
    • (1989) Computing , vol.41 , pp. 335-348
    • Hoffmann, W.1
  • 20
    • 0002168778 scopus 로고
    • Solving linear least squares problems by Gram-Schmidt orthogonalization
    • Björck Å. Solving linear least squares problems by Gram-Schmidt orthogonalization. BIT 1967; 7:1-21.
    • (1967) BIT , vol.7 , pp. 1-21
    • Björck, Å.1
  • 21
    • 0000585494 scopus 로고
    • Numerics of Gram-Schmidt orthogonalization
    • Björck Å. Numerics of Gram-Schmidt orthogonalization. Linear Algebra and its Applications 1994; 197/198:297-315.
    • (1994) Linear Algebra and Its Applications , vol.197-198 , pp. 297-315
    • Björck, Å.1
  • 23
    • 0001876101 scopus 로고
    • Solution of augmented linear systems using orthogonal factorizations
    • Björck Å, Paige CC. Solution of augmented linear systems using orthogonal factorizations. BIT 1994; 34:1-24.
    • (1994) BIT , vol.34 , pp. 1-24
    • Björck, Å.1    Paige, C.C.2
  • 24
    • 0001473420 scopus 로고
    • Iterative refinement of linear least squares solutions
    • Björck Å. Iterative refinement of linear least squares solutions. BIT 1967; 7:257-278.
    • (1967) BIT , vol.7 , pp. 257-278
    • Björck, Å.1
  • 25
    • 0000904936 scopus 로고
    • Modifications of the normal equations method that are numerically stable
    • Golub GH, Van Dooren P (eds), NATO ASI Series. Springer: Berlin
    • Foster LV. Modifications of the normal equations method that are numerically stable. In Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms, Golub GH, Van Dooren P (eds), NATO ASI Series. Springer: Berlin, 1991; 501-512.
    • (1991) Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms , pp. 501-512
    • Foster, L.V.1
  • 26
    • 0000924593 scopus 로고
    • Numerical methods for solving linear least squares problems
    • Golub GH. Numerical methods for solving linear least squares problems. Numerische Mathematik 1965; 7: 206-216.
    • (1965) Numerische Mathematik , vol.7 , pp. 206-216
    • Golub, G.H.1
  • 27
    • 0012096207 scopus 로고
    • Note on the iterative refinement of least squares solution
    • Golub GH, Wilkinson JH. Note on the iterative refinement of least squares solution. Numerische Mathematik 1966; 9:139-148.
    • (1966) Numerische Mathematik , vol.9 , pp. 139-148
    • Golub, G.H.1    Wilkinson, J.H.2
  • 28
    • 0000673625 scopus 로고
    • Linear least squares solutions by Householder transformations
    • Businger P, Golub GH. Linear least squares solutions by Householder transformations. Numerische Mathematik 1965; 7:269-276.
    • (1965) Numerische Mathematik , vol.7 , pp. 269-276
    • Businger, P.1    Golub, G.H.2
  • 29
    • 0002671024 scopus 로고
    • Stability analysis of the method of semi-normal equations for least squares problems
    • Björck Å. Stability analysis of the method of semi-normal equations for least squares problems. Linear Algebra and its Applications 1987; 88/89:31-48.
    • (1987) Linear Algebra and Its Applications , vol.88-89 , pp. 31-48
    • Björck, Å.1
  • 30
    • 4043130870 scopus 로고    scopus 로고
    • A modified iterative refinement scheme
    • Dax A. A modified iterative refinement scheme. SIAM Journal on Scientific Computing 2004; 25:1199-1213.
    • (2004) SIAM Journal on Scientific Computing , vol.25 , pp. 1199-1213
    • Dax, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.