메뉴 건너뛰기




Volumn 34, Issue 2-4, 2003, Pages 339-353

Block Krylov subspace methods for large algebraic Riccati equations

Author keywords

Block Arnoldi; Krylov subspaces; Low rank approximations; Riccati equations

Indexed keywords


EID: 4043084911     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:NUMA.0000005349.18793.28     Document Type: Article
Times cited : (55)

References (29)
  • 2
    • 0021618667 scopus 로고
    • Generalized eigenproblem algorithms and software for algebraic Riccati equations
    • W.F. Arnold, III and A.J. Laub, Generalized eigenproblem algorithms and software for algebraic Riccati equations, Proc. 72 (1984) 1746-1754.
    • (1984) Proc. , vol.72 , pp. 1746-1754
    • Arnold III, W.F.1    Laub, A.J.2
  • 3
    • 0032338141 scopus 로고    scopus 로고
    • Using the matrix sign function to compute invariant subspaces
    • Z. Bai and J. Demmel, Using the matrix sign function to compute invariant subspaces, SIAM J. Anal. Appl. 19 (1998) 205-225.
    • (1998) SIAM J. Anal. Appl. , vol.19 , pp. 205-225
    • Bai, Z.1    Demmel, J.2
  • 4
    • 0031673797 scopus 로고    scopus 로고
    • An exact line search method for solving generalized continous algebraic Riccati equations
    • P. Benner and R. Byers, An exact line search method for solving generalized continous algebraic Riccati equations, IEEE Trans. Automat. Control 43(1) (1998) 101-107.
    • (1998) IEEE Trans. Automat. Control. , vol.43 , Issue.1 , pp. 101-107
    • Benner, P.1    Byers, R.2
  • 5
    • 0040689412 scopus 로고    scopus 로고
    • An implicitly restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem
    • P. Benner and H. Faßbender, An implicitly restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem, Linear Algebra Appl. 263 (1997) 75-111.
    • (1997) Linear Algebra Appl. , vol.263 , pp. 75-111
    • Benner, P.1    Faßbender, H.2
  • 6
    • 0003418313 scopus 로고
    • A collection of benchmark examples for the numerical solution of algebraic Riccati equations I: Continuous-time case
    • Fak. f. Mathematik, TU Chemnitz-Zwickau, Chemnitz, Germany
    • P. Benner, A. Laub and V. Mehrmann, A collection of benchmark examples for the numerical solution of algebraic Riccati equations I: Continuous-time case, Technical Report SPC 95-22, Fak. f. Mathematik, TU Chemnitz-Zwickau, Chemnitz, Germany (1995).
    • (1995) Technical Report SPC 95-22
    • Benner, P.1    Laub, A.2    Mehrmann, V.3
  • 7
    • 0022914040 scopus 로고    scopus 로고
    • A symplectic QR-like algorithm for the solution of the real algebraic Riccati equations
    • A. Bunse-Gerstner and V. Mehrmann, A symplectic QR-like algorithm for the solution of the real algebraic Riccati equations, IEEE Trans. Automat. Control 43(1) (1998) 1104-1113.
    • (1998) IEEE Trans. Automat. Control , vol.43 , Issue.1 , pp. 1104-1113
    • Bunse-Gerstner, A.1    Mehrmann, V.2
  • 9
    • 38249038136 scopus 로고
    • Solving the algebraic Riccati equation with the matrix sign function
    • R. Byers, Solving the algebraic Riccati equation with the matrix sign function, Linear Algebra Appl. 85 (1987) 267-279.
    • (1987) Linear Algebra Appl. , vol.85 , pp. 267-279
    • Byers, R.1
  • 11
    • 27544508073 scopus 로고    scopus 로고
    • Model reduction of state space systems via an implicitly restarted Lanczos method
    • E.J. Grimme, D.C. Sorenson and P. Van Dooren, Model reduction of state space systems via an implicitly restarted Lanczos method, Numer. Algorithms 12 (1996) 1-31.
    • (1996) Numer. Algorithms , vol.12 , pp. 1-31
    • Grimme, E.J.1    Sorenson, D.C.2    Van Dooren, P.3
  • 12
    • 0028447254 scopus 로고
    • Numerical solution of the discrete-time periodic Riccati equation
    • J.J. Hench and A.J. Laub, Numerical solution of the discrete-time periodic Riccati equation, IEEE Trans. Automat. Control 39 (1994) 1197-1209.
    • (1994) IEEE Trans. Automat. Control , vol.39 , pp. 1197-1209
    • Hench, J.J.1    Laub, A.J.2
  • 13
    • 0028377922 scopus 로고
    • Krylov subspace methods for solving large Lyapunov equations
    • I.M. Jaimoukha and E.M. Kasenally, Krylov subspace methods for solving large Lyapunov equations, SIAM J. Numer. Anal. 31 (1994) 227-251.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 227-251
    • Jaimoukha, I.M.1    Kasenally, E.M.2
  • 15
    • 84914965022 scopus 로고
    • On an iterative technique for Riccati equation computations
    • D.L. Kleinman, On an iterative technique for Riccati equation computations, IEEE Trans. Automat. Control 13 (1968) 114-115.
    • (1968) IEEE Trans. Automat. Control , vol.13 , pp. 114-115
    • Kleinman, D.L.1
  • 17
    • 0018681625 scopus 로고
    • A Schur method for solving algebraic Riccati equations
    • A.J. Laub, A Schur method for solving algebraic Riccati equations, IEEE Trans. Automat. Control 24 (1979) 913-921.
    • (1979) IEEE Trans. Automat. Control , vol.24 , pp. 913-921
    • Laub, A.J.1
  • 19
    • 0019069037 scopus 로고    scopus 로고
    • Linear model reduction and solution of the algebraic Riccati equation by use of the sign function
    • D.J. Roberts, Linear model reduction and solution of the algebraic Riccati equation by use of the sign function, Internat. J. Control 32 (1998) 677-687.
    • (1998) Internat. J. Control , vol.32 , pp. 677-687
    • Roberts, D.J.1
  • 20
    • 0001422598 scopus 로고
    • Rational Krylov sequence methods for eigenvalue computations
    • A. Ruhe, Rational Krylov sequence methods for eigenvalue computations, Linear Algebra Appl. 58 (1984) 391-405.
    • (1984) Linear Algebra Appl. , vol.58 , pp. 391-405
    • Ruhe, A.1
  • 22
    • 21144469414 scopus 로고
    • Block Arnoldi and Davidson methods for unsymmetric large eigenvalue problems
    • M. Sadkane, Block Arnoldi and Davidson methods for unsymmetric large eigenvalue problems, Numer. Math. 64 (1993) 687-706.
    • (1993) Numer. Math. , vol.64 , pp. 687-706
    • Sadkane, M.1
  • 23
    • 0000322706 scopus 로고
    • Implicit application of polynomial filters in a k-step Arnoldi method
    • D.C. Sorensen, Implicit application of polynomial filters in a k-step Arnoldi method, SIAM J. Matrix Anal. Appl. 13(1) (1992) 357-387.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , Issue.1 , pp. 357-387
    • Sorensen, D.C.1
  • 25
    • 0032341236 scopus 로고    scopus 로고
    • Perturbation theory for algebraic Riccati equation
    • J.-G. Sun, Perturbation theory for algebraic Riccati equation, SIAM J. Matrix Anal. Appl. 19(1) (1998) 39-65.
    • (1998) SIAM J. Matrix Anal. Appl. , vol.19 , Issue.1 , pp. 39-65
    • Sun, J.-G.1
  • 26
    • 0031508420 scopus 로고    scopus 로고
    • Residual bounds of approximate solutions of the algebraic Riccati equation
    • J.-G. Sun, Residual bounds of approximate solutions of the algebraic Riccati equation, Numer. Math. 76 (1997) 249-263.
    • (1997) Numer. Math. , vol.76 , pp. 249-263
    • Sun, J.-G.1
  • 27
    • 0000669144 scopus 로고
    • A generalized eigenvalue approach for solving Riccati equations
    • P. Van Dooren, A generalized eigenvalue approach for solving Riccati equations, SIAM J. Sci. Statist. Comput. 2 (1981) 121-135.
    • (1981) SIAM J. Sci. Statist. Comput. , vol.2 , pp. 121-135
    • Van Dooren, P.1
  • 28
    • 0000059741 scopus 로고
    • A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix
    • C.F. Van Loan, A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix, Linear Algebra Appl. 16 (1984) 233-251.
    • (1984) Linear Algebra Appl. , vol.16 , pp. 233-251
    • Van Loan, C.F.1
  • 29
    • 0001042840 scopus 로고
    • On a matrix Riccati equation of stochastic control
    • W.M. Wonham, On a matrix Riccati equation of stochastic control, SIAM J. Control 6 (1968) 681-697.
    • (1968) SIAM J. Control , vol.6 , pp. 681-697
    • Wonham, W.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.