메뉴 건너뛰기




Volumn 21, Issue 4, 1999, Pages 1199-1221

Tensor methods for large, sparse nonlinear least squares problems

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; FINITE DIFFERENCE METHOD; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; NONLINEAR EQUATIONS; OPTIMIZATION;

EID: 0033293030     PISSN: 10648275     EISSN: None     Source Type: None    
DOI: 10.1137/S1064827596297549     Document Type: Article
Times cited : (12)

References (24)
  • 1
    • 0022060730 scopus 로고
    • Variational methods for non-linear least squares
    • M. AL-BAALI AND R. FLETCHER, Variational methods for non-linear least squares, J. Oper. Res. Soc., 36 (1985), pp. 405-421.
    • (1985) J. Oper. Res. Soc. , vol.36 , pp. 405-421
    • Al-Baali, M.1    Fletcher, R.2
  • 2
    • 0001351705 scopus 로고
    • On the augmented system approach to sparse least-squares problems
    • M. ARIOLI, I. S. DUFF, AND P. P. M. RIJK, On the augmented system approach to sparse least-squares problems, Numer. Math., 55 (1989), pp. 667-684.
    • (1989) Numer. Math. , vol.55 , pp. 667-684
    • Arioli, M.1    Duff, I.S.2    Rijk, P.P.M.3
  • 4
    • 0001473420 scopus 로고
    • Iterative refinement of linear least squares solutions
    • Å. BJÖRCK, Iterative refinement of linear least squares solutions, BIT, 7 (1967), pp. 257-278.
    • (1967) BIT , vol.7 , pp. 257-278
    • Björck, Å.1
  • 7
    • 0031152378 scopus 로고    scopus 로고
    • Algorithm 768: TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least squares problems using tensor methods
    • A. BOUARICHA AND R. B. SCHNABEL, Algorithm 768: TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least squares problems using tensor methods, ACM Trans. Math. Software, 23 (1997), pp. 174-195.
    • (1997) ACM Trans. Math. Software , vol.23 , pp. 174-195
    • Bouaricha, A.1    Schnabel, R.B.2
  • 8
    • 0016072422 scopus 로고
    • Partial pivoting strategies for symmetric matrices
    • J. R. BUNCH, Partial pivoting strategies for symmetric matrices, SIAM J. Numer. Anal., 11 (1974), pp. 521-528.
    • (1974) SIAM J. Numer. Anal. , vol.11 , pp. 521-528
    • Bunch, J.R.1
  • 9
    • 0021488613 scopus 로고
    • Fortran subroutines for estimating sparse Jacobian matrices
    • T. F. COLEMAN, B. S. GARBOW, AND J. J. MORÉ, Fortran subroutines for estimating sparse Jacobian matrices, ACM Trans. Math. Software, 10 (1984) pp. 346-347.
    • (1984) ACM Trans. Math. Software , vol.10 , pp. 346-347
    • Coleman, T.F.1    Garbow, B.S.2    Moré, J.J.3
  • 11
    • 0000421410 scopus 로고
    • Estimation of sparse Jacobian matrices and graph coloring problems
    • T. F. COLEMAN AND J. J. MORÉ, Estimation of sparse Jacobian matrices and graph coloring problems, SIAM J. Numer. Anal., 20 (1983). pp. 187-209.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 187-209
    • Coleman, T.F.1    Moré, J.J.2
  • 12
    • 84952419741 scopus 로고
    • On the estimation of sparse Jacobian matrices
    • A. M. CURTIS, M. J. D. POWELL, AND J. K. REID, On the estimation of sparse Jacobian matrices, J. Inst. Math. Appl, 13 (1974), pp. 117-120.
    • (1974) J. Inst. Math. Appl , vol.13 , pp. 117-120
    • Curtis, A.M.1    Powell, M.J.D.2    Reid, J.K.3
  • 16
    • 0040731298 scopus 로고
    • A comparison of some methods for the solution of sparse overdetermined system
    • I. S. DUFF AND J. K. REID, A comparison of some methods for the solution of sparse overdetermined system, J. Inst. Math. Appl., 17 (1975), pp. 267-280.
    • (1975) J. Inst. Math. Appl. , vol.17 , pp. 267-280
    • Duff, I.S.1    Reid, J.K.2
  • 17
    • 34250084281 scopus 로고
    • Local convergence analysis of tensor methods for nonlinear equations
    • D. FENG, P. FRANK, AND R. B. SCHNABEL, Local convergence analysis of tensor methods for nonlinear equations, Math. Programming, 62 (1993), pp. 427-459.
    • (1993) Math. Programming , vol.62 , pp. 427-459
    • Feng, D.1    Frank, P.2    Schnabel, R.B.3
  • 18
    • 0000847769 scopus 로고
    • Least squares computation by givens transformations without squares roots
    • W. M. GENTLEMAN, Least squares computation by givens transformations without squares roots, J. Inst. Math. Appl., 12 (1973), pp. 329-336.
    • (1973) J. Inst. Math. Appl. , vol.12 , pp. 329-336
    • Gentleman, W.M.1
  • 20
    • 0000924593 scopus 로고
    • Numerical methods for solving linear least squares problems
    • G. H. GOLUB, Numerical methods for solving linear least squares problems, Numer. Math., 7 (1965), pp. 206-216.
    • (1965) Numer. Math. , vol.7 , pp. 206-216
    • Golub, G.H.1
  • 21
    • 0343013184 scopus 로고
    • Extended applications of the sparse tableau approach-finite elements and least squares
    • W. R. Spillers, ed., North-Holland, Amsterdam
    • G. D. HACHTEL, Extended applications of the sparse tableau approach-finite elements and least squares, in Basic Questions of Design Theory, W. R. Spillers, ed., North-Holland, Amsterdam, 1974.
    • (1974) Basic Questions of Design Theory
    • Hachtel, G.D.1
  • 22
    • 0014827294 scopus 로고
    • The least squares problem and pseudo-inverses
    • G. PETERS AND J. H. WILKINSON, The least squares problem and pseudo-inverses, Comput. J., 13 (1970), pp. 309-316.
    • (1970) Comput. J. , vol.13 , pp. 309-316
    • Peters, G.1    Wilkinson, J.H.2
  • 23
    • 0021510543 scopus 로고
    • Tensor methods for nonlinear equations
    • R. B. SCHNABEL AND P. D. FRANK, Tensor methods for nonlinear equations, SIAM J. Numer. Anal., 21 (1984), pp. 815-843.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 815-843
    • Schnabel, R.B.1    Frank, P.D.2
  • 24
    • 0022205528 scopus 로고
    • A modular system of algorithms of unconstrained minimization
    • R. B. SCHNABEL, J. E. KOONTZ, AND B. E. WEISS, A modular system of algorithms of unconstrained minimization, ACM Trans. Math. Software, 11 (1985), pp. 419-440.
    • (1985) ACM Trans. Math. Software , vol.11 , pp. 419-440
    • Schnabel, R.B.1    Koontz, J.E.2    Weiss, B.E.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.