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Volumn 43, Issue 3, 2005, Pages 1321-1347

Tensor-Krylov methods for solving large-scale systems of nonlinear equations

Author keywords

Curvilinear line search; Krylov subspace methods; Linesearch; Newton's method; Nonlinear systems; Tensor methods

Indexed keywords

CURVILINEAR LINE-SEARCH; KRYLOV SUBSPACE METHODS; LINESEARCH; NEWTON'S METHOD; TENSOR METHODS;

EID: 33745465892     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/040607095     Document Type: Article
Times cited : (24)

References (31)
  • 3
    • 85140870730 scopus 로고    scopus 로고
    • On the performance of tensor methods for solving ill-conditioned problems
    • submitted
    • B. W. BADER AND R. B. SCHNABEL, On the performance of tensor methods for solving ill-conditioned problems, SIAM J. Sci. Comput., submitted.
    • SIAM J. Sci. Comput.
    • Bader, B.W.1    Schnabel, R.B.2
  • 4
    • 2342488828 scopus 로고    scopus 로고
    • Curvilinear linesearch for tensor methods
    • B. W. BADER AND R. B. SCHNABEL, Curvilinear linesearch for tensor methods, SIAM J. Sci, Comput., 25 (2003), pp. 604-622.
    • (2003) SIAM J. Sci, Comput. , vol.25 , pp. 604-622
    • Bader, B.W.1    Schnabel, R.B.2
  • 6
    • 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
  • 7
    • 33750393487 scopus 로고
    • Reduced storage methods in stiff ODE systems
    • P. N. BROWN AND A. C. HINDMARSH, Reduced storage methods in stiff ODE systems, J. Appl. Math. Comp., 31 (1989), pp. 40-91.
    • (1989) J. Appl. Math. Comp. , vol.31 , pp. 40-91
    • Brown, P.N.1    Hindmarsh, A.C.2
  • 8
    • 0000977352 scopus 로고
    • Hybrid Krylov methods for nonlinear systems of equations
    • P. N. BROWN AND Y. SAAD, Hybrid Krylov methods for nonlinear systems of equations, SIAM J. Sci. Statist. Comput., 11 (1990), pp. 450-481.
    • (1990) SIAM J. Sci. Statist. Comput. , vol.11 , pp. 450-481
    • Brown, P.N.1    Saad, Y.2
  • 9
    • 0000873548 scopus 로고
    • Newton-like pseudo-arclength methods for computing simple turning points
    • T. F. CHAN, Newton-like pseudo-arclength methods for computing simple turning points, SIAM J. Sci. Statist. Comput., 5 (1984), pp. 135-148.
    • (1984) SIAM J. Sci. Statist. Comput. , vol.5 , pp. 135-148
    • Chan, T.F.1
  • 10
    • 0031488469 scopus 로고    scopus 로고
    • Deflated and augmented Krylov subspace techniques
    • A. CHAPMAN AND Y. SAAD, Deflated and augmented Krylov subspace techniques, Numer. Linear Algebra Appl., 4 (1997), pp. 43-66.
    • (1997) Numer. Linear Algebra Appl. , vol.4 , pp. 43-66
    • Chapman, A.1    Saad, Y.2
  • 11
    • 0001261109 scopus 로고
    • Convergence rate for Newton's method at singular points
    • D. W. DECKER, H. B. KELLER, AND C. T. KELLEY, Convergence rate for Newton's method at singular points, SIAM J. Numer. Anal., 20 (1983), pp. 296-314.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 296-314
    • Decker, D.W.1    Keller, H.B.2    Kelley, C.T.3
  • 12
    • 0002689824 scopus 로고
    • Newton's method at singular points I
    • D. W. DECKER AND C. T. KELLEY, Newton's method at singular points I, SIAM J. Numer. Anal., 17 (1980), pp. 66-70.
    • (1980) SIAM J. Numer. Anal. , vol.17 , pp. 66-70
    • Decker, D.W.1    Kelley, C.T.2
  • 13
    • 0002689826 scopus 로고
    • Newton's method at singular points II
    • D. W. DECKER AND C. T. KELLEY, Newton's method at singular points II, SIAM J. Numer. Anal., 17 (1980), pp. 465-471.
    • (1980) SIAM J. Numer. Anal. , vol.17 , pp. 465-471
    • Decker, D.W.1    Kelley, C.T.2
  • 16
    • 0003176174 scopus 로고    scopus 로고
    • Choosing the forcing terms in an inexact Newton method
    • S. C. EISENSTAT AND H. F. WALKER, Choosing the forcing terms in an inexact Newton method, SIAM J. Sci. Comput., 17 (1996), pp. 16-32.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 16-32
    • Eisenstat, S.C.1    Walker, H.F.2
  • 17
    • 34250084281 scopus 로고
    • Local convergence analysis of tensor methods for nonlinear equations
    • D. FENG, P. D. FRANK, AND R. B. SCHNABEL, Local convergence analysis of tensor methods for nonlinear equations, Math. Program., 62 (1993), pp. 427-459.
    • (1993) Math. Program. , vol.62 , pp. 427-459
    • Feng, D.1    Frank, P.D.2    Schnabel, R.B.3
  • 18
    • 0031285892 scopus 로고    scopus 로고
    • Tensor-GMRES method for large systems of nonlinear equations
    • D. FENG AND T. H. PULLIAM, Tensor-GMRES method for large systems of nonlinear equations, SIAM J. Optim., 7 (1997), pp. 757-779.
    • (1997) SIAM J. Optim. , vol.7 , pp. 757-779
    • Feng, D.1    Pulliam, T.H.2
  • 21
    • 0001281959 scopus 로고
    • On Newton's method for singular problems
    • G. W. REDDIEN, On Newton's method for singular problems, SIAM J. Numer. Anal., 15 (1978), pp. 993-996.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 993-996
    • Reddien, G.W.1
  • 22
    • 84968508607 scopus 로고
    • Implementation aspects of band Lanczos algorithms for computation of eigenvalues of large sparse symmetric matrices
    • A. RUHE, Implementation aspects of band Lanczos algorithms for computation of eigenvalues of large sparse symmetric matrices, Math. Comput., 33 (1979), pp. 680-687.
    • (1979) Math. Comput. , vol.33 , pp. 680-687
    • Ruhe, A.1
  • 23
    • 84966222159 scopus 로고
    • Krylov subspace methods for solving unsymmetric linear systems
    • Y. SAAD, Krylov subspace methods for solving unsymmetric linear systems, Math. Comp., 37 (1981), pp. 105-126.
    • (1981) Math. Comp. , vol.37 , pp. 105-126
    • Saad, Y.1
  • 24
    • 84985408358 scopus 로고
    • ILUT: A dual threshold incomplete ILU preconditioned
    • Y. SAAD, ILUT: A dual threshold incomplete ILU preconditioned Numer. Linear Algebra Appl., 1 (1994), pp. 387-402.
    • (1994) Numer. Linear Algebra Appl. , vol.1 , pp. 387-402
    • Saad, Y.1
  • 25
    • 0031534369 scopus 로고    scopus 로고
    • Analysis of augmented Krylov subspace methods
    • Y. SAAD, Analysis of augmented Krylov subspace methods, SIAM J. Matrix Anal. Appl., 18 (1997), pp. 435-449.
    • (1997) SIAM J. Matrix Anal. Appl. , vol.18 , pp. 435-449
    • Saad, Y.1
  • 26
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Y. SAAD AND M. H. SCHULTZ, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856-869.
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 27
    • 0003997220 scopus 로고    scopus 로고
    • MPSalsa, a finite element computer program for reacting flow problems, part 2 - User's guide
    • Sandia National Laboratories, Albuquerque, NM
    • A. G. SALINGER, K. D. DEVINE, G. L. HENNIGAN, H. K. MOFFAT, S. A. HUTCHINSON, AND J. N. SHADID, MPSalsa, A Finite Element Computer Program for Reacting Flow Problems, Part 2 - User's Guide, Technical report SAND96-2331, Sandia National Laboratories, Albuquerque, NM, 1996.
    • (1996) Technical Report , vol.SAND96-2331
    • Salinger, A.G.1    Devine, K.D.2    Hennigan, G.L.3    Moffat, H.K.4    Hutchinson, S.A.5    Shadid, J.N.6
  • 28
    • 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
  • 29
    • 0033267340 scopus 로고    scopus 로고
    • A fully-coupled Newton-Krylov solution method for parallel unstructured finite element fluid flow, heat and mass transfer simulations
    • J. N. SHADID, A fully-coupled Newton-Krylov solution method for parallel unstructured finite element fluid flow, heat and mass transfer simulations, Int. J. Comput. Fluid Dyn., 12 (1999), pp. 199-211.
    • (1999) Int. J. Comput. Fluid Dyn. , vol.12 , pp. 199-211
    • Shadid, J.N.1
  • 30
    • 0001176429 scopus 로고    scopus 로고
    • An inexact Newton method for fully coupled solution of the Navier-Stokes equations with heat and mass transport
    • J. N. SHADID, R. S. TUMINARO, AND H. F. WALKER, An inexact Newton method for fully coupled solution of the Navier-Stokes equations with heat and mass transport, J. Comput. Phys., 137 (1997), pp. 155-185.
    • (1997) J. Comput. Phys. , vol.137 , pp. 155-185
    • Shadid, J.N.1    Tuminaro, R.S.2    Walker, H.F.3
  • 31
    • 0037055748 scopus 로고    scopus 로고
    • On backtracking failure in Newton-GMRES methods with a demonstration for the Navier-Stokes equations
    • R. S. TUMINARO, H. F. WALKER, AND J. N. SHADID, On backtracking failure in Newton-GMRES methods with a demonstration for the Navier-Stokes equations, J. Comput. Phys., 180 (2002), pp. 549-558.
    • (2002) J. Comput. Phys. , vol.180 , pp. 549-558
    • Tuminaro, R.S.1    Walker, H.F.2    Shadid, J.N.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.