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Volumn 26, Issue 5, 2005, Pages 1598-1619

Block-diagonal and constraint preconditioners for nonsymmetric indefinite linear systems. Part I: Theory

Author keywords

Constrained optimization; Eigenvalue bounds; Indefinite systems; Krylov subspace methods; Mesh flattening; Preconditioning; Saddle point systems

Indexed keywords

CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; MATRIX ALGEBRA; OPTIMIZATION; PROBLEM SOLVING;

EID: 20044380099     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827502411006     Document Type: Article
Times cited : (89)

References (35)
  • 1
    • 34249955392 scopus 로고
    • A class of iterative methods for solving saddle point problems
    • R. E. BANK, B. D. WELFERT, AND H. YSERENTANT, A class of iterative methods for solving saddle point problems, Numer. Math., 56 (1990), pp. 645-666.
    • (1990) Numer. Math. , vol.56 , pp. 645-666
    • Bank, R.E.1    Welfert, B.D.2    Yserentant, H.3
  • 2
    • 0003854283 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge, UK
    • D. BRAESS, Finite Elements, 2nd ed., Cambridge University Press, Cambridge, UK, 2001.
    • (2001) Finite Elements, 2nd Ed.
    • Braess, D.1
  • 3
    • 0036954879 scopus 로고    scopus 로고
    • A subspace cascadic multigrid method for mortar elements
    • D. BRAESS, P. DEUFLHARD, AND K. LIPNIKOV, A subspace cascadic multigrid method for mortar elements, Computing, 69 (2002), pp. 205-225.
    • (2002) Computing , vol.69 , pp. 205-225
    • Braess, D.1    Deuflhard, P.2    Lipnikov, K.3
  • 4
    • 0031070105 scopus 로고    scopus 로고
    • An efficient smoother for the Stokes problem
    • D. BRAESS AND R. SARAZIN, An efficient smoother for the Stokes problem, Appl. Numer. Math., 23 (1997), pp. 3-19.
    • (1997) Appl. Numer. Math. , vol.23 , pp. 3-19
    • Braess, D.1    Sarazin, R.2
  • 5
    • 25444479938 scopus 로고    scopus 로고
    • Block-diagonal preconditioned for indefinite linear algebraic systems. Part I: Theory
    • Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL
    • E. DE STURLER AND J. LIESEN, Block-Diagonal Preconditioned for Indefinite Linear Algebraic Systems. Part I: Theory, Tech. Report UIUCDCS-R-2002-2279, Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL, 2002.
    • (2002) Tech. Report , vol.UIUCDCS-R-2002-2279
    • De Sturler, E.1    Liesen, J.2
  • 6
    • 84966216063 scopus 로고
    • The numerical solution of equality constrained quadratic programming problems
    • N. DYN AND W. E. FERGUSON, JR., The numerical solution of equality constrained quadratic programming problems, Math. Comp., 41 (1983), pp. 165-170.
    • (1983) Math. Comp. , vol.41 , pp. 165-170
    • Dyn, N.1    Ferguson Jr., W.E.2
  • 8
    • 0033279287 scopus 로고    scopus 로고
    • Preconditioning for the steady-state Navier-Stokes equations with low viscosity
    • H. C. ELMAN, Preconditioning for the steady-state Navier-Stokes equations with low viscosity, SIAM J. Sci. Comput., 20 (1999), pp. 1299-1316.
    • (1999) SIAM J. Sci. Comput. , vol.20 , pp. 1299-1316
    • Elman, H.C.1
  • 9
    • 0028741633 scopus 로고
    • Inexact and preconditioned Uzawa algorithms for saddle point problems
    • H. C. ELMAN AND G. H. GOLUB, Inexact and preconditioned Uzawa algorithms for saddle point problems, SIAM J. Numer. Anal., 31 (1994), pp. 1645-1661.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1645-1661
    • Elman, H.C.1    Golub, G.H.2
  • 10
    • 0002308279 scopus 로고
    • Conjugate gradient methods for indefinite systems
    • Proceedings of the 6th Biennial Dundee Conference on Numerical Analysis, G. Watson, ed., Springer-Verlag, Berlin
    • R. FLETCHER, Conjugate gradient methods for indefinite systems, in Proceedings of the 6th Biennial Dundee Conference on Numerical Analysis, G. Watson, ed., Lecture Notes in Math. 506, Springer-Verlag, Berlin, 1976, pp. 73-89.
    • (1976) Lecture Notes in Math. , vol.506 , pp. 73-89
    • Fletcher, R.1
  • 12
    • 0002211239 scopus 로고    scopus 로고
    • An iteration for indefinite systems and its application to the Navier-Stokes equations
    • G. H. GOLUB AND A. J. WATHEN, An iteration for indefinite systems and its application to the Navier-Stokes equations, SIAM J. Sci. Comput., 19 (1998), pp. 530-539.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 530-539
    • Golub, G.H.1    Wathen, A.J.2
  • 13
    • 0036344992 scopus 로고    scopus 로고
    • On the solution of equality constrained quadratic programming problems arising in optimization
    • N. I. M. GOULD, M. E. HRIBAR, AND J. NOCEDAL, On the solution of equality constrained quadratic programming problems arising in optimization, SIAM J. Sci. Comput., 23 (2001), pp. 1376-1395.
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 1376-1395
    • Gould, N.I.M.1    Hribar, M.E.2    Nocedal, J.3
  • 14
    • 0003241196 scopus 로고    scopus 로고
    • Iterative methods for solving linear systems
    • SIAM, Philadelphia
    • A. GREENBAUM, Iterative Methods for Solving Linear Systems, Frontiers in Appl. Math. 17, SIAM, Philadelphia, 1997.
    • (1997) Frontiers in Appl. Math. , vol.17
    • Greenbaum, A.1
  • 16
    • 0035616487 scopus 로고    scopus 로고
    • A nearly optimal preconditioner for the Navier-Stokes equations
    • L. HEMMINGSSON-FRÄNDÉN AND A. WATHEN, A nearly optimal preconditioner for the Navier-Stokes equations, Numer. Linear Algebra Appl., 8 (2001), pp. 229-243.
    • (2001) Numer. Linear Algebra Appl. , vol.8 , pp. 229-243
    • Hemmingsson-Frändén, L.1    Wathen, A.2
  • 17
    • 0034145598 scopus 로고    scopus 로고
    • Constraint preconditioning for indefinite linear systems
    • C. KELLER, N. I. M. GOULD, AND A. J. WATHEN, Constraint preconditioning for indefinite linear systems, SIAM J. Matrix Anal. Appl., 21 (2000), pp. 1300-1317.
    • (2000) SIAM J. Matrix Anal. Appl. , vol.21 , pp. 1300-1317
    • Keller, C.1    Gould, N.I.M.2    Wathen, A.J.3
  • 18
    • 0036205721 scopus 로고    scopus 로고
    • On block preconditioned for nonsymmetric saddle point problems
    • P. KRZYŻANOWSKI, On block preconditioned for nonsymmetric saddle point problems, SIAM J. Sci. Comput., 23 (2001), pp. 157-169.
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 157-169
    • Krzyzanowski, P.1
  • 21
    • 0345293940 scopus 로고    scopus 로고
    • Indefinitely preconditioned inexact Newton method for large sparse equality constrained non-linear programming problems
    • L. LUKŠAN AND J. VLČEK, Indefinitely preconditioned inexact Newton method for large sparse equality constrained non-linear programming problems, Numer. Linear Algebra Appl., 5 (1998), pp. 219-247.
    • (1998) Numer. Linear Algebra Appl. , vol.5 , pp. 219-247
    • Lukšan, L.1    Vlček, J.2
  • 23
    • 0034497397 scopus 로고    scopus 로고
    • A note on preconditioning for indefinite linear systems
    • M. F. MURPHY, G. H. GOLUB, AND A. J. WATHEN, A note on preconditioning for indefinite linear systems, SIAM J. Sci. Comput., 21 (2000), pp. 1969-1972.
    • (2000) SIAM J. Sci. Comput. , vol.21 , pp. 1969-1972
    • Murphy, M.F.1    Golub, G.H.2    Wathen, A.J.3
  • 24
    • 0034368563 scopus 로고    scopus 로고
    • Block-diagonal and indefinite symmetric preconditioned for mixed finite element formulations
    • I. PERUGIA AND V. SIMONCINI, Block-diagonal and indefinite symmetric preconditioned for mixed finite element formulations, Numer. Linear Algebra Appl., 7 (2000), pp. 585-616.
    • (2000) Numer. Linear Algebra Appl. , vol.7 , pp. 585-616
    • Perugia, I.1    Simoncini, V.2
  • 25
    • 0033296578 scopus 로고    scopus 로고
    • Linear algebra methods in a mixed approximation of magnetostatic problems
    • I. PERUGIA, V. SIMONCINI, AND M. ARIOLI, Linear algebra methods in a mixed approximation of magnetostatic problems, SIAM J. Sci. Comput., 21 (1999), pp. 1085-1101.
    • (1999) SIAM J. Sci. Comput. , vol.21 , pp. 1085-1101
    • Perugia, I.1    Simoncini, V.2    Arioli, M.3
  • 26
    • 0344950439 scopus 로고    scopus 로고
    • Krylov subspace methods for saddle point problems with indefinite preconditioning
    • M. ROZLOŽNÍK AND V. SIMONCINI, Krylov subspace methods for saddle point problems with indefinite preconditioning, SIAM J. Matrix Anal. Appl., 24 (2002), pp. 368-391.
    • (2002) SIAM J. Matrix Anal. Appl. , vol.24 , pp. 368-391
    • Rozložník, M.1    Simoncini, V.2
  • 27
    • 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
  • 29
    • 0035174536 scopus 로고    scopus 로고
    • Surface parameterization for meshing using angle-based flattening
    • A. SHEFFER AND E. DE STURLER, Surface parameterization for meshing using angle-based flattening, Engineering with Computers, 17 (2001), pp. 326-337; also available online from Springer at http://link.springer.de/link/service/ journals/00366/tocs/t1017003.htm.
    • (2001) Engineering with Computers , vol.17 , pp. 326-337
    • Sheffer, A.1    De Sturler, E.2
  • 30
    • 0141435696 scopus 로고    scopus 로고
    • Smoothing an overlay grid to minimize linear distortion in texture mapping
    • A. SHEFFER AND E. DE STURLER, Smoothing an overlay grid to minimize linear distortion in texture mapping, ACM Trans. Graphics, 21 (2002), pp. 874-890.
    • (2002) ACM Trans. Graphics , vol.21 , pp. 874-890
    • Sheffer, A.1    De Sturler, E.2
  • 31
    • 0035281553 scopus 로고    scopus 로고
    • Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow
    • D. SILVESTER, H. ELMAN, D. KAY, AND A. WATHEN, Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow, J. Comput. Appl. Math., 128 (2001), pp. 261-279.
    • (2001) J. Comput. Appl. Math. , vol.128 , pp. 261-279
    • Silvester, D.1    Elman, H.2    Kay, D.3    Wathen, A.4
  • 32
    • 0028517184 scopus 로고
    • Fast iterative solution of stabilised Stokes systems Part II. Using general block preconditioned
    • D. SILVESTER AND A. WATHEN, Fast iterative solution of stabilised Stokes systems Part II. Using general block preconditioned, SIAM J. Numer. Anal., 31 (1994), pp. 1352-1367.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1352-1367
    • Silvester, D.1    Wathen, A.2
  • 35
    • 0027606774 scopus 로고
    • Fast iterative solution of stabilised Stokes systems Part I. Using simple diagonal preconditioned
    • A. WATHEN AND D. SILVESTER, Fast iterative solution of stabilised Stokes systems Part I. Using simple diagonal preconditioned, SIAM J. Numer. Anal., 30 (1993), pp. 630-649.
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 630-649
    • Wathen, A.1    Silvester, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.