메뉴 건너뛰기




Volumn 415, Issue 2-3, 2006, Pages 344-358

Projection methods for large Lyapunov matrix equations

Author keywords

Block Arnoldi; Global Arnoldi; Krylov subspaces; Lyapunov matrix equation

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; CONTROL THEORY; LINEAR ALGEBRA; MATRIX ALGEBRA; PROBLEM SOLVING;

EID: 33745469648     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2004.11.004     Document Type: Article
Times cited : (104)

References (27)
  • 1
    • 33748104810 scopus 로고    scopus 로고
    • A.C. Antoulas, D.C. Sorensen, Projection methods for balanced model reduction, Technical Report, Rice University, Houston, TX, 2001
  • 2
    • 84976855597 scopus 로고
    • Solution of the matrix equation AX + XB = C
    • Bartels R.H., and Stewart G.W. Solution of the matrix equation AX + XB = C. Comm. ACM 15 (1972) 820-826
    • (1972) Comm. ACM , vol.15 , pp. 820-826
    • Bartels, R.H.1    Stewart, G.W.2
  • 3
    • 0033412866 scopus 로고    scopus 로고
    • Solving stable generalized Lyapunov equations with the matrix sign function
    • Benner P., and Quintana-Ortí E. Solving stable generalized Lyapunov equations with the matrix sign function. Numer. Alg. 20 (1999) 75-100
    • (1999) Numer. Alg. , vol.20 , pp. 75-100
    • Benner, P.1    Quintana-Ortí, E.2
  • 4
    • 51249161441 scopus 로고
    • Krylov space methods on state-space control models
    • Boley D.L. Krylov space methods on state-space control models. Circ. Syst. Signal Process. 13 (1994) 733-758
    • (1994) Circ. Syst. Signal Process. , vol.13 , pp. 733-758
    • Boley, D.L.1
  • 5
    • 0000875808 scopus 로고
    • Contollability, observability and solution of AX - XB = C
    • de Souza E., and Bhattacharyya S.P. Contollability, observability and solution of AX - XB = C. Linear Algebra Appl. 39 (1981) 167-188
    • (1981) Linear Algebra Appl. , vol.39 , pp. 167-188
    • de Souza, E.1    Bhattacharyya, S.P.2
  • 6
    • 0036254232 scopus 로고    scopus 로고
    • Block Krylov subspace methods for solving large Sylvester equations
    • El Guennouni A., Jbilou K., and Riquet A.J. Block Krylov subspace methods for solving large Sylvester equations. Numer. Alg. 29 (2002) 75-96
    • (2002) Numer. Alg. , vol.29 , pp. 75-96
    • El Guennouni, A.1    Jbilou, K.2    Riquet, A.J.3
  • 9
    • 0000567621 scopus 로고
    • Numerical solution of the stable, nonnegative definite Lyapunov equation
    • Hammarling S.J. Numerical solution of the stable, nonnegative definite Lyapunov equation. IMA J. Numer. Anal. 2 (1982) 303-323
    • (1982) IMA J. Numer. Anal. , vol.2 , pp. 303-323
    • Hammarling, S.J.1
  • 10
    • 0015368704 scopus 로고
    • Resultants and the solution of AX - XB = -C
    • Hartwig R.E. Resultants and the solution of AX - XB = -C. SIAM J. Appl. Math. 23 1 (1972) 104-117
    • (1972) SIAM J. Appl. Math. , vol.23 , Issue.1 , pp. 104-117
    • Hartwig, R.E.1
  • 11
    • 38249011246 scopus 로고
    • Krylov subspace methods for the Sylvester equation
    • Hu D.Y., and Reichel L. Krylov subspace methods for the Sylvester equation. Linear Algebra Appl. 174 (1992) 283-314
    • (1992) Linear Algebra Appl. , vol.174 , pp. 283-314
    • Hu, D.Y.1    Reichel, L.2
  • 12
    • 0028377922 scopus 로고
    • Krylov subspace methods for solving large Lyapunov equations
    • Jaimoukha I.M., and Kasenally E.M. Krylov subspace methods for solving large Lyapunov equations. SIAM J. Matrix Anal. Appl. 31 1 (1994) 227-251
    • (1994) SIAM J. Matrix Anal. Appl. , vol.31 , Issue.1 , pp. 227-251
    • Jaimoukha, I.M.1    Kasenally, E.M.2
  • 13
    • 0005279528 scopus 로고
    • Oblique projection methods for large scale model reduction
    • Jaimoukha I.M., and Kasenally E.M. Oblique projection methods for large scale model reduction. SIAM J. Matrix Anal. Appl. 16 2 (1995) 602-627
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , Issue.2 , pp. 602-627
    • Jaimoukha, I.M.1    Kasenally, E.M.2
  • 14
    • 33748105331 scopus 로고    scopus 로고
    • K. Jbilou, On Krylov subspace methods for solving the matrix Sylvester equation AX - XB = C, Technical report LMPA (71), Université du Littoral, Calais, France, 1998
  • 15
    • 0033197189 scopus 로고    scopus 로고
    • Global FOM and GMRES algorithms for matrix equations
    • Jbilou K., Messaoudi A., and Sadok H. Global FOM and GMRES algorithms for matrix equations. Appl. Num. Math. 31 (1999) 49-63
    • (1999) Appl. Num. Math. , vol.31 , pp. 49-63
    • Jbilou, K.1    Messaoudi, A.2    Sadok, H.3
  • 17
    • 85165533029 scopus 로고    scopus 로고
    • J.-R. Li, F. Wang, J. White, An efficient Lyapunov equation-based approach for generating reduced-order models of interconnect, in: 36th IEEE/ACM Design Automation Conference, New Orleans, LA, 1999, pp. 1-6.
  • 18
    • 0002909988 scopus 로고
    • Solution of Lyapunov equations by alternating direction implicit iteration
    • Lu A., and Wachspress E.L. Solution of Lyapunov equations by alternating direction implicit iteration. Comput. Math. Appl. 21 (1991) 43-58
    • (1991) Comput. Math. Appl. , vol.21 , pp. 43-58
    • Lu, A.1    Wachspress, E.L.2
  • 19
    • 0019533482 scopus 로고
    • Principal component analysis in linear systems: controllability, observability and model reduction
    • Moore B.C. Principal component analysis in linear systems: controllability, observability and model reduction. IEEE Trans. Auto. Control AC 26 (1981) 17-31
    • (1981) IEEE Trans. Auto. Control AC , vol.26 , pp. 17-31
    • Moore, B.C.1
  • 20
    • 0033295674 scopus 로고    scopus 로고
    • A cyclic low rank Smith method for large sparse Lyapunov equations
    • Penzl T. A cyclic low rank Smith method for large sparse Lyapunov equations. SIAM J. Sci. Comput. 21 4 (2000) 1401-1418
    • (2000) SIAM J. Sci. Comput. , vol.21 , Issue.4 , pp. 1401-1418
    • Penzl, T.1
  • 21
    • 0000175612 scopus 로고
    • Numerical solution of large Lyapunov equations
    • Kaashoek M.A., Van Shuppen J.H., and Ran A.C. (Eds), Birkhaüser, Boston
    • Saad Y. Numerical solution of large Lyapunov equations. In: Kaashoek M.A., Van Shuppen J.H., and Ran A.C. (Eds). Signal Processing, Scattering, Operator Theory and Numerical Methods (1990), Birkhaüser, Boston 503-511
    • (1990) Signal Processing, Scattering, Operator Theory and Numerical Methods , pp. 503-511
    • Saad, Y.1
  • 23
    • 21144469414 scopus 로고
    • Block Arnoldi and Davidson methods for unsymmetric large eigenvalue problems
    • Sadkane M. 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
  • 24
    • 0041540457 scopus 로고    scopus 로고
    • Convergence properties of block GMRES and matrix polynomials
    • Simoncini V., and Gallopoulos E. Convergence properties of block GMRES and matrix polynomials. Linear Algebra Appl. 247 (1996) 97-119
    • (1996) Linear Algebra Appl. , vol.247 , pp. 97-119
    • Simoncini, V.1    Gallopoulos, E.2
  • 25
    • 0009139884 scopus 로고
    • Matrix calculations for Liapunov quadratic forms
    • Smith R.A. Matrix calculations for Liapunov quadratic forms. J. Different. Eqs. 2 (1966) 208-217
    • (1966) J. Different. Eqs. , vol.2 , pp. 208-217
    • Smith, R.A.1
  • 26
    • 0002700172 scopus 로고    scopus 로고
    • Gramian based model reduction of large-scale dynamical systems
    • Chapman and Hall, CRC Press, London
    • Van Dooren P. Gramian based model reduction of large-scale dynamical systems. Numerical Analysis (2000), Chapman and Hall, CRC Press, London 231-247
    • (2000) Numerical Analysis , pp. 231-247
    • Van Dooren, P.1
  • 27
    • 0000509808 scopus 로고
    • The sensitivity of the matrix exponential
    • Van Loan C. The sensitivity of the matrix exponential. SIAM J. Numer. Anal. 14 (1977) 971-981
    • (1977) SIAM J. Numer. Anal. , vol.14 , pp. 971-981
    • Van Loan, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.