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Volumn 49, Issue 1, 2009, Pages 93-111

Algebraically stable general linear methods and the G-matrix

Author keywords

Algebraic stability; Discrete algebraic Riccati equation; General linear methods

Indexed keywords


EID: 61849112771     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10543-008-0207-7     Document Type: Article
Times cited : (17)

References (15)
  • 1
    • 0014476598 scopus 로고
    • Conditions for positive and non-negative definiteness in terms of pseudoinverses
    • A. Albert 1969 Conditions for positive and non-negative definiteness in terms of pseudoinverses SIAM J. Appl. Math. 17 434 440
    • (1969) SIAM J. Appl. Math. , vol.17 , pp. 434-440
    • Albert, A.1
  • 2
    • 0023287926 scopus 로고
    • High order algebraically stable multistep Runge-Kutta methods
    • K. Burrage 1987 High order algebraically stable multistep Runge-Kutta methods SIAM J. Numer. Anal. 24 106 115
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 106-115
    • Burrage, K.1
  • 3
    • 0001356367 scopus 로고
    • Non-linear stability of a general class of differential equation methods
    • K. Burrage J.C. Butcher 1980 Non-linear stability of a general class of differential equation methods BIT 20 185 203
    • (1980) BIT , vol.20 , pp. 185-203
    • Burrage, K.1    Butcher, J.C.2
  • 4
    • 84968503738 scopus 로고
    • The order of numerical methods for ordinary differential equations
    • J.C. Butcher 1973 The order of numerical methods for ordinary differential equations Math. Comput. 27 793 806
    • (1973) Math. Comput. , vol.27 , pp. 793-806
    • Butcher, J.C.1
  • 5
    • 33645019289 scopus 로고
    • The equivalence of algebraic stability and AN-stability
    • J.C. Butcher 1987 The equivalence of algebraic stability and AN-stability BIT 27 510 533
    • (1987) BIT , vol.27 , pp. 510-533
    • Butcher, J.C.1
  • 6
    • 38249003919 scopus 로고
    • Diagonally-implicit multi-stage integration methods
    • J.C. Butcher 1993 Diagonally-implicit multi-stage integration methods Appl. Numer. Math. 11 347 363
    • (1993) Appl. Numer. Math. , vol.11 , pp. 347-363
    • Butcher, J.C.1
  • 7
    • 33646816440 scopus 로고    scopus 로고
    • General linear methods
    • J.C. Butcher 2006 General linear methods Acta Numer. 15 157 256
    • (2006) Acta Numer. , vol.15 , pp. 157-256
    • Butcher, J.C.1
  • 8
    • 33645038609 scopus 로고    scopus 로고
    • Linear multistep methods as irreducible general linear methods
    • J.C. Butcher A.T. Hill 2006 Linear multistep methods as irreducible general linear methods BIT 46 5 19
    • (2006) BIT , vol.46 , pp. 5-19
    • Butcher, J.C.1    Hill, A.T.2
  • 9
    • 0001074434 scopus 로고
    • Diagonally implicit general linear methods for ordinary differential equations
    • J.C. Butcher Z. Jackiewicz 1993 Diagonally implicit general linear methods for ordinary differential equations BIT 33 452 472
    • (1993) BIT , vol.33 , pp. 452-472
    • Butcher, J.C.1    Jackiewicz, Z.2
  • 10
    • 0030263281 scopus 로고    scopus 로고
    • Construction of diagonally implicit general linear methods for ordinary differential equations
    • J.C. Butcher Z. Jackiewicz 1996 Construction of diagonally implicit general linear methods for ordinary differential equations Appl. Numer. Math. 21 385 415
    • (1996) Appl. Numer. Math. , vol.21 , pp. 385-415
    • Butcher, J.C.1    Jackiewicz, Z.2
  • 11
    • 33646821967 scopus 로고
    • Technical Report No. 25, Computer Science Department, University of Auckland, New Zealand
    • Dekker, K.: Algebraic stability of general linear methods. Technical Report No. 25, Computer Science Department, University of Auckland, New Zealand (1981)
    • (1981) Algebraic Stability of General Linear Methods
    • Dekker, K.1
  • 12
    • 0032216891 scopus 로고    scopus 로고
    • Newton's method for the discrete algebraic Riccati equations when the closed-loop matrix has an eigenvalue on the unit circle
    • C.-H. Guo 1998 Newton's method for the discrete algebraic Riccati equations when the closed-loop matrix has an eigenvalue on the unit circle SIAM J. Matrix Anal. Appl. 20 279 294
    • (1998) SIAM J. Matrix Anal. Appl. , vol.20 , pp. 279-294
    • Guo, C.-H.1
  • 14
    • 33744730778 scopus 로고    scopus 로고
    • Nonlinear stability of general linear methods
    • A.T. Hill 2006 Nonlinear stability of general linear methods Numer. Math. 103 611 629
    • (2006) Numer. Math. , vol.103 , pp. 611-629
    • Hill, A.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.