메뉴 건너뛰기




Volumn 30, Issue 3-4, 2002, Pages 241-258

Preconditioned spectral gradient method

Author keywords

Multidimensional scaling; Nonmonotone line search; Poisson type equations; Preconditioning techniques; Spectral gradient method

Indexed keywords


EID: 0036377266     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020181927999     Document Type: Article
Times cited : (22)

References (29)
  • 1
    • 38149145405 scopus 로고
    • Solution of nonlinear Poisson-type equations
    • B.M. Averick and J.M. Ortega, Solution of nonlinear Poisson-type equations, Appl. Numer. Math. 8 (1991) 443-455.
    • (1991) Appl. Numer. Math. , vol.8 , pp. 443-455
    • Averick, B.M.1    Ortega, J.M.2
  • 2
    • 0141467952 scopus 로고
    • Fast solution of nonlinear Poisson-type equations
    • B.M. Averick and J.M. Ortega, Fast solution of nonlinear Poisson-type equations, SIAM J. Sci. Comput. 14 (1993) 44-48.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 44-48
    • Averick, B.M.1    Ortega, J.M.2
  • 3
    • 0021825930 scopus 로고
    • A survey of preconditioned iterative methods for linear systems of algebraic equations
    • O. Axelsson, A survey of preconditioned iterative methods for linear systems of algebraic equations, Bit 25 (1985) 166-187.
    • (1985) Bit , vol.25 , pp. 166-187
    • Axelsson, O.1
  • 5
    • 0000350662 scopus 로고
    • Newton's method applied to finite difference approximations for the steady-state compressible Navier-Stokes equations
    • H.E. Bailey and R.M. Beam, Newton's method applied to finite difference approximations for the steady-state compressible Navier-Stokes equations, J. Comput. Phys. 93 (1991) 108-127.
    • (1991) J. Comput. Phys. , vol.93 , pp. 108-127
    • Bailey, H.E.1    Beam, R.M.2
  • 6
    • 0001531895 scopus 로고
    • Two point step size gradient methods
    • J. Barzilai and J.M. Borwein, Two point step size gradient methods, IMA J. Numer. Anal. 8 (1988) 141-148.
    • (1988) IMA J. Numer. Anal. , vol.8 , pp. 141-148
    • Barzilai, J.1    Borwein, J.M.2
  • 7
    • 0033237258 scopus 로고    scopus 로고
    • Restricted optimization: A clue to fast and accurate implementation of the common reflection surface method
    • E.G. Birgin, R. Biloti, M. Tygel and L.T. Santos, Restricted optimization: A clue to fast and accurate implementation of the common reflection surface method, J. Appl. Geophys. 42 (1999) 143-155.
    • (1999) J. Appl. Geophys. , vol.42 , pp. 143-155
    • Birgin, E.G.1    Biloti, R.2    Tygel, M.3    Santos, L.T.4
  • 8
    • 0001384606 scopus 로고    scopus 로고
    • Estimation of the optical constants and the thickness of thin films using unconstrained optimization
    • E.G. Birgin, I. Chambouleyron and J.M. Martínez, Estimation of the optical constants and the thickness of thin films using unconstrained optimization, J. Comput. Phys. 151 (1999) 862-880.
    • (1999) J. Comput. Phys. , vol.151 , pp. 862-880
    • Birgin, E.G.1    Chambouleyron, I.2    Martínez, J.M.3
  • 9
    • 0000222244 scopus 로고    scopus 로고
    • Automatic differentiation and spectral projected gradient methods for optimal control problems
    • E.G. Birgin and Y.G. Evtushenko, Automatic differentiation and spectral projected gradient methods for optimal control problems, Optim. Methods Software 10 (1998) 125-146.
    • (1998) Optim. Methods Software , vol.10 , pp. 125-146
    • Birgin, E.G.1    Evtushenko, Y.G.2
  • 10
    • 0141467950 scopus 로고    scopus 로고
    • A spectral conjugate gradient method for unconstrained optimization
    • E.G. Birgin and J.M. Martínez, A spectral conjugate gradient method for unconstrained optimization, Appl. Math. Optim. 43 (2001) 117-128.
    • (2001) Appl. Math. Optim. , vol.43 , pp. 117-128
    • Birgin, E.G.1    Martínez, J.M.2
  • 12
    • 0343795911 scopus 로고    scopus 로고
    • Low cost optimization techniques for solving the nonlinear seismic reflection tomography problem
    • Z. Castillo, D. Cores and M. Raydan, Low cost optimization techniques for solving the nonlinear seismic reflection tomography problem, Optim. Engrg. 1 (2000) 155-169.
    • (2000) Optim. Engrg. , vol.1 , pp. 155-169
    • Castillo, Z.1    Cores, D.2    Raydan, M.3
  • 13
    • 0034351853 scopus 로고    scopus 로고
    • A fast and global two point low storage optimization technique for tracing rays in 2D and 3D isotropic media
    • D. Cores, G. Fung and R. Michelena, A fast and global two point low storage optimization technique for tracing rays in 2D and 3D isotropic media, J. Appl. Geophys. 45 (2000) 273-287.
    • (2000) J. Appl. Geophys. , vol.45 , pp. 273-287
    • Cores, D.1    Fung, G.2    Michelena, R.3
  • 14
    • 0000922470 scopus 로고
    • Molecular conformations from distance matrices
    • W. Glunt, T.L. Hayden and M. Raydan, Molecular conformations from distance matrices, J. Comput. Chem. 14 (1993) 114-120.
    • (1993) J. Comput. Chem. , vol.14 , pp. 114-120
    • Glunt, W.1    Hayden, T.L.2    Raydan, M.3
  • 15
    • 84986533367 scopus 로고
    • Preconditioners for distance matrix algorithms
    • W. Glunt, T.L. Hayden and M. Raydan, Preconditioners for distance matrix algorithms, J. Comput. Chem. 15 (1994) 227-232.
    • (1994) J. Comput. Chem. , vol.15 , pp. 227-232
    • Glunt, W.1    Hayden, T.L.2    Raydan, M.3
  • 16
    • 0022766519 scopus 로고
    • A nonmonotone line search technique for Newton's method
    • L. Grippo, F. Lampariello and S. Lucidi, A nonmonotone line search technique for Newton's method, SIAM J. Numer. Anal. 23 (19) 707-716, 1986.
    • (1986) SIAM J. Numer. Anal. , vol.23 , Issue.19 , pp. 707-716
    • Grippo, L.1    Lampariello, F.2    Lucidi, S.3
  • 18
    • 0141691200 scopus 로고    scopus 로고
    • Fast algorithms for multidimensional scaling: A comparison of majorization and spectral gradient methods
    • University of Leiden, Leiden, Netherlands
    • P.J.F. Groenen, W. Glunt and T.L. Hayden, Fast algorithms for multidimensional scaling: A comparison of majorization and spectral gradient methods, Technical Report, Data Theory Department, University of Leiden, Leiden, Netherlands (1996).
    • (1996) Technical Report, Data Theory Department
    • Groenen, P.J.F.1    Glunt, W.2    Hayden, T.L.3
  • 19
    • 0030490277 scopus 로고    scopus 로고
    • The tunneling method for global optimization in multidimensional scaling
    • P.J.F. Groenen and W.J. Heiser, The tunneling method for global optimization in multidimensional scaling, Psychometrika 61 (1996) 529-550.
    • (1996) Psychometrika , vol.61 , pp. 529-550
    • Groenen, P.J.F.1    Heiser, W.J.2
  • 20
    • 0033478830 scopus 로고    scopus 로고
    • Global optimization in least-squares multidimensional scaling by distance smoothing
    • P.J.F. Groenen, W.J. Heiser and J.J. Meulman, Global optimization in least-squares multidimensional scaling by distance smoothing, J. Classification 16 (1999) 225-254.
    • (1999) J. Classification , vol.16 , pp. 225-254
    • Groenen, P.J.F.1    Heiser, W.J.2    Meulman, J.J.3
  • 21
    • 0032376620 scopus 로고    scopus 로고
    • The solution of the metric stress and stress problems in multidimensional scaling using Newton's method
    • A.J. Kearsley, R.A. Tapia and M.W. Trosset, The solution of the metric stress and stress problems in multidimensional scaling using Newton's method, Comput. Statist. 13(3) (1998) 369-396.
    • (1998) Comput. Statist. , vol.13 , Issue.3 , pp. 369-396
    • Kearsley, A.J.1    Tapia, R.A.2    Trosset, M.W.3
  • 22
    • 21444432174 scopus 로고    scopus 로고
    • The preconditioned Barzilai-Borwein method for the numerical solution of partial differential equations
    • B. Molina and M. Raydan, The preconditioned Barzilai-Borwein method for the numerical solution of partial differential equations, Numer. Algorithms 13 (1996) 45-60.
    • (1996) Numer. Algorithms , vol.13 , pp. 45-60
    • Molina, B.1    Raydan, M.2
  • 23
    • 0000044081 scopus 로고    scopus 로고
    • Determination of thickness and optical constants of a-Si:H films from transmittance data
    • M. Mulato, I. Chambouleyron, E.G. Birgin and J.M. Martínez, Determination of thickness and optical constants of a-Si:H films from transmittance data, Appl. Phys. Lett. 77 (2000) 2133-2135.
    • (2000) Appl. Phys. Lett. , vol.77 , pp. 2133-2135
    • Mulato, M.1    Chambouleyron, I.2    Birgin, E.G.3    Martínez, J.M.4
  • 24
    • 0009399116 scopus 로고    scopus 로고
    • Conjugate gradient methods and nonlinear optimization
    • eds. L. Adams and J.L. Nazareth, AMS-IMS-SIAM Joint Summer Research Conference (SIAM, Philadelphia, PA)
    • J. Nocedal, Conjugate gradient methods and nonlinear optimization, in: Linear and Nonlinear Conjugate Gradient Related Methods, eds. L. Adams and J.L. Nazareth, AMS-IMS-SIAM Joint Summer Research Conference (SIAM, Philadelphia, PA, 1996) pp. 9-23.
    • (1996) Linear and Nonlinear Conjugate Gradient Related Methods , pp. 9-23
    • Nocedal, J.1
  • 25
    • 0011739235 scopus 로고
    • On the Barzilai and Borwein choice of steplength for the gradient method
    • M. Raydan, On the Barzilai and Borwein choice of steplength for the gradient method, IMA J. Numer. Anal. 13 (1993) 321-326.
    • (1993) IMA J. Numer. Anal. , vol.13 , pp. 321-326
    • Raydan, M.1
  • 26
    • 0031542191 scopus 로고    scopus 로고
    • The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem
    • M. Raydan, The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem, SIAM J. Optim. 7 (1997) 26-33.
    • (1997) SIAM J. Optim. , vol.7 , pp. 26-33
    • Raydan, M.1
  • 27
    • 0141802778 scopus 로고
    • On preconditioned conjugate gradient methods
    • eds. R.R. Meyer, O.L. Mangasarian and S.M. Robinson (Academic Press, New York)
    • D.F. Shanno, On preconditioned conjugate gradient methods, in: Nonlinear Programming, Vol. 4, eds. R.R. Meyer, O.L. Mangasarian and S.M. Robinson (Academic Press, New York, 1981) pp. 201-221.
    • (1981) Nonlinear Programming , vol.4 , pp. 201-221
    • Shanno, D.F.1
  • 28
    • 0011514701 scopus 로고    scopus 로고
    • Numerical algorithms for MDS
    • eds. R. Klar and P. Opitz (Springer, Berlin)
    • M.W. Trosset, Numerical algorithms for MDS, in: Classification and Knowledge Organization, eds. R. Klar and P. Opitz (Springer, Berlin, 1997) pp. 80-92.
    • (1997) Classification and Knowledge Organization , pp. 80-92
    • Trosset, M.W.1
  • 29
    • 0000121535 scopus 로고
    • Searching conformational space with the spectral distance geometry algorithm
    • C. Wells, W. Glunt and T.L. Hayden, Searching conformational space with the spectral distance geometry algorithm, J. Molecular Structure (Theochem) 308 (1994) 263-271.
    • (1994) J. Molecular Structure (Theochem) , vol.308 , pp. 263-271
    • Wells, C.1    Glunt, W.2    Hayden, T.L.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.