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Underlying one-step methods and nonautonomous stability of general linear methods
Conditioning and relative error propagation in linear autonomous ordinary differential equations
Dipartimento di Matematica e Geoscienze, Università di Trieste, Via Valerio 12/1, 34127, Trieste, Italy |
In this paper, we study the relative error propagation in the solution of linear autonomous ordinary differential equations with respect to perturbations in the initial value. We also consider equations with a constant forcing term and a nonzero equilibrium. The study is carried out for equations defined by normal matrices.
References:
[1] |
A. H. Al-Mohy and N. J. Higham,
Computing the Fréchet derivative of the matrix exponential, with an application to condition number estimation, SIAM J. Matrix Anal. Appl., 30 (2009), 1639-1657.
doi: 10.1137/080716426. |
[2] |
F. Burgisser and F. Cucker, Condition, Springer 2013.
doi: 10.1007/978-3-642-38896-5. |
[3] |
R. Grone, C. R. Johnson, E. M. Sa and H. Wolkowicz,
Normal matrices, Linear Algebra and its Applications, 87 (1987), 213-225.
doi: 10.1016/0024-3795(87)90168-6. |
[4] |
G. Golub and C. F. Van Loan, Matrix Computations, The John Hopkins University Press, third edition 1996. |
[5] |
E. Hairer, S. Norsett and G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems, Springer-Verlag Berlin Heidelberg, Second Revised Edition, 1993. |
[6] |
N. J. Higham, Functions of Matrices, Theory and Computation, Siam, 2008.
doi: 10.1137/1.9780898717778. |
[7] |
N. J. Higham and A. H. Al-Mohy,
Computing matrix functions, Acta Numerica, 19 (2010), 159-208.
doi: 10.1017/S0962492910000036. |
[8] |
B. Kagstrom,
Bounds and perturbations for the matrix exponential, BIT, 17 (1977), 39-57.
|
show all references
References:
[1] |
A. H. Al-Mohy and N. J. Higham,
Computing the Fréchet derivative of the matrix exponential, with an application to condition number estimation, SIAM J. Matrix Anal. Appl., 30 (2009), 1639-1657.
doi: 10.1137/080716426. |
[2] |
F. Burgisser and F. Cucker, Condition, Springer 2013.
doi: 10.1007/978-3-642-38896-5. |
[3] |
R. Grone, C. R. Johnson, E. M. Sa and H. Wolkowicz,
Normal matrices, Linear Algebra and its Applications, 87 (1987), 213-225.
doi: 10.1016/0024-3795(87)90168-6. |
[4] |
G. Golub and C. F. Van Loan, Matrix Computations, The John Hopkins University Press, third edition 1996. |
[5] |
E. Hairer, S. Norsett and G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems, Springer-Verlag Berlin Heidelberg, Second Revised Edition, 1993. |
[6] |
N. J. Higham, Functions of Matrices, Theory and Computation, Siam, 2008.
doi: 10.1137/1.9780898717778. |
[7] |
N. J. Higham and A. H. Al-Mohy,
Computing matrix functions, Acta Numerica, 19 (2010), 159-208.
doi: 10.1017/S0962492910000036. |
[8] |
B. Kagstrom,
Bounds and perturbations for the matrix exponential, BIT, 17 (1977), 39-57.
|







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