메뉴 건너뛰기




Volumn 36, Issue 2-3, 2007, Pages 249-270

Using constraint preconditioners with regularized saddle-point problems

Author keywords

Indefinite linear systems; Krylov subspace methods; Preconditioning

Indexed keywords

CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; OPTIMIZATION; PROBLEM SOLVING; SPECTRUM ANALYSIS;

EID: 34248198456     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-006-9004-x     Document Type: Article
Times cited : (23)

References (24)
  • 1
    • 34248217528 scopus 로고    scopus 로고
    • Axelsson, O., Barker, V.A.: Finite Element Solution of Boundary Value Problems. Theory and Computation, Classics in Applied Mathematics, 35. SIAM, Philadelphia (2001). Reprint of the 1984 original
    • Axelsson, O., Barker, V.A.: Finite Element Solution of Boundary Value Problems. Theory and Computation, Classics in Applied Mathematics, vol. 35. SIAM, Philadelphia (2001). Reprint of the 1984 original
  • 2
    • 20044390432 scopus 로고    scopus 로고
    • Numerical solution of saddle point problems
    • Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numer. 14, 1-137 (2005)
    • (2005) Acta Numer , vol.14 , pp. 1-137
    • Benzi, M.1    Golub, G.H.2    Liesen, J.3
  • 3
    • 3543086890 scopus 로고    scopus 로고
    • Preconditioning indefinite systems in interior point methods for optimization
    • Bergamaschi, L., Gondzio, J., Zilli, G.: Preconditioning indefinite systems in interior point methods for optimization. Comput. Optim. Appl. 28, 149-171 (2004)
    • (2004) Comput. Optim. Appl , vol.28 , pp. 149-171
    • Bergamaschi, L.1    Gondzio, J.2    Zilli, G.3
  • 4
    • 34547596785 scopus 로고    scopus 로고
    • Cafieri, S., D'Apuzzo, M., De Simone, V., di Serafino, D.: On the iterative solution of KKT systems in potential reduction software for large-scale quadratic problems. Technical Report 09/2004, Dept. of Mathematics, Second University of Naples (December 2004). Comput. Optim. Appl. (to appear)
    • Cafieri, S., D'Apuzzo, M., De Simone, V., di Serafino, D.: On the iterative solution of KKT systems in potential reduction software for large-scale quadratic problems. Technical Report 09/2004, Dept. of Mathematics, Second University of Naples (December 2004). Comput. Optim. Appl. (to appear)
  • 5
    • 34248199918 scopus 로고    scopus 로고
    • Dollar, H.S.: Constraint-style preconditioners for regularized saddle-point problems. Technical Report 3/2006, Dept. of Mathematics, University of Reading (March 2006). SIAM J. Matrix Anal. Appl. (to appear)
    • Dollar, H.S.: Constraint-style preconditioners for regularized saddle-point problems. Technical Report 3/2006, Dept. of Mathematics, University of Reading (March 2006). SIAM J. Matrix Anal. Appl. (to appear)
  • 8
    • 33845515988 scopus 로고    scopus 로고
    • Iterative solution of augmented systems arising in interior methods
    • Technical Report NA-05-03, University of California, San Diego August
    • Forsgren, A., Gill, P.E., Griffin, J.D.: Iterative solution of augmented systems arising in interior methods. Technical Report NA-05-03, University of California, San Diego (August 2005)
    • (2005)
    • Forsgren, A.1    Gill, P.E.2    Griffin, J.D.3
  • 11
    • 0001087725 scopus 로고
    • On the accurate determination of search directions for simple differentiable penalty functions
    • Gould, N.I.M.: On the accurate determination of search directions for simple differentiable penalty functions. IMA J. Numer. Anal. 6, 357-372 (1986)
    • (1986) IMA J. Numer. Anal , vol.6 , pp. 357-372
    • Gould, N.I.M.1
  • 12
    • 0036344992 scopus 로고    scopus 로고
    • On the solution of equality constrained quadratic programming problems arising in optimization
    • Gould, N.I.M., Hribar, M.E., Nocedal, J.: On the solution of equality constrained quadratic programming problems arising in optimization. SIAM J. Sci. Comput. 23, 1376-1395 (2001)
    • (2001) SIAM J. Sci. Comput , vol.23 , pp. 1376-1395
    • Gould, N.I.M.1    Hribar, M.E.2    Nocedal, J.3
  • 13
    • 2442598318 scopus 로고    scopus 로고
    • CUTEr and SifDec: A constrained and unconstrained testing environment, revisited
    • Gould, N.I.M., Orban, D., Toint, P.L.: CUTEr and SifDec: a constrained and unconstrained testing environment, revisited. ACM Trans. Math. Software 29, 373-394 (2003)
    • (2003) ACM Trans. Math. Software , vol.29 , pp. 373-394
    • Gould, N.I.M.1    Orban, D.2    Toint, P.L.3
  • 14
    • 0003241196 scopus 로고    scopus 로고
    • Iterative Methods for Solving Linear Systems
    • SIAM, Philadelphia
    • Greenbaum, A.: Iterative Methods for Solving Linear Systems. Frontiers in Applied Mathematics, vol. 17. SIAM, Philadelphia (1997)
    • (1997) Frontiers in Applied Mathematics , vol.17
    • Greenbaum, A.1
  • 15
    • 0041049302 scopus 로고    scopus 로고
    • Any nonincreasing convergence curve is possible for GMRES
    • Greenbaum, A., Pták, V., Strakoš, Z.: Any nonincreasing convergence curve is possible for GMRES. SIAM J. Matrix Anal. Appl. 17, 465-469 (1996)
    • (1996) SIAM J. Matrix Anal. Appl , vol.17 , pp. 465-469
    • Greenbaum, A.1    Pták, V.2    Strakoš, Z.3
  • 16
    • 0034145598 scopus 로고    scopus 로고
    • Constraint preconditioning for indefinite linear systems
    • Keller, C., Gould, N.I.M., Wathen, A.J.: Constraint preconditioning for indefinite linear systems. SIAM J. Matrix Anal. Appl. 21, 1300-1317 (2000)
    • (2000) SIAM J. Matrix Anal. Appl , vol.21 , pp. 1300-1317
    • Keller, C.1    Gould, N.I.M.2    Wathen, A.J.3
  • 17
    • 0345293940 scopus 로고    scopus 로고
    • Indefinitely preconditioned inexact Newton method for large sparse equality constrained non-linear programming problems
    • Lukšan, L., Vlček, J.: Indefinitely preconditioned inexact Newton method for large sparse equality constrained non-linear programming problems. Numer. Linear Algebra Appl. 5, 219-247 (1998)
    • (1998) Numer. Linear Algebra Appl , vol.5 , pp. 219-247
    • Lukšan, L.1    Vlček, J.2
  • 18
    • 0034368563 scopus 로고    scopus 로고
    • Block-diagonal and indefinite symmetric preconditioners for mixed finite element formulations
    • Perugia, I., Simoncini, V.: Block-diagonal and indefinite symmetric preconditioners for mixed finite element formulations. Numer. Linear Algebra Appl. 7, 585-616 (2000)
    • (2000) Numer. Linear Algebra Appl , vol.7 , pp. 585-616
    • Perugia, I.1    Simoncini, V.2
  • 19
    • 0344950439 scopus 로고    scopus 로고
    • Krylov subspace methods for saddle point problems with indefinite preconditioning
    • Rozložník, M., Simoncini, V.: Krylov subspace methods for saddle point problems with indefinite preconditioning. SIAM J. Matrix Anal. Appl. 24, 368-391 (2002)
    • (2002) SIAM J. Matrix Anal. Appl , vol.24 , pp. 368-391
    • Rozložník, M.1    Simoncini, V.2
  • 21
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Saad, Y., Schultz, M.H.: GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7, 856-869 (1986)
    • (1986) SIAM J. Sci. Stat. Comput , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 22
    • 0035359418 scopus 로고    scopus 로고
    • The quadratic eigenvalue problem
    • Tisseur, F., Meerbergen, K.: The quadratic eigenvalue problem. SIAM Rev. 43, 235-286 (2001)
    • (2001) SIAM Rev , vol.43 , pp. 235-286
    • Tisseur, F.1    Meerbergen, K.2
  • 23
    • 3142570751 scopus 로고    scopus 로고
    • Block preconditioners for symmetric indefinite linear systems
    • Toh, K.-C., Phoon, K.-K., Chan, S.-H.: Block preconditioners for symmetric indefinite linear systems. Int. J. Numer. Methods Eng. 60, 1361-1381 (2004)
    • (2004) Int. J. Numer. Methods Eng , vol.60 , pp. 1361-1381
    • Toh, K.-C.1    Phoon, K.-K.2    Chan, S.-H.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.