Abstract
Acceleration techniques for iterative methods for linear systems of both static (Qy = b) and dynamic (y′ = Qy + g(t)) type are analyzed. A new splitting Q = M - N, where M is block-Toeplitz is proposed. In the static case considerable improvement is observed, while in the dynamic case this preconditioning results only in a slightly faster waveform relaxation scheme than the traditional block-Jacobi dynamic iteration method in the case of linear systems approximating heat equation in one or two dimensions. It is shown that the static analysis does not predict correctly the optimal value of the parameters introduced for the dynamic case, but that a spectral analysis does.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 51-74 |
| Number of pages | 24 |
| Journal | Linear Algebra and Its Applications |
| Volume | 279 |
| Issue number | 1-3 |
| State | Published - Aug 15 1998 |
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Keywords
- Accelerating of convergence
- Iterative methods
- Overlapping
- Preconditioning
- Splitting
- Waveform relaxation method
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
Cite this
Block-Toeplitz preconditioning for static and dynamic linear systems. / Burrage, K.; Jackiewicz, Zdzislaw; Welfert, Bruno.
In: Linear Algebra and Its Applications, Vol. 279, No. 1-3, 15.08.1998, p. 51-74.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Block-Toeplitz preconditioning for static and dynamic linear systems
AU - Burrage, K.
AU - Jackiewicz, Zdzislaw
AU - Welfert, Bruno
PY - 1998/8/15
Y1 - 1998/8/15
N2 - Acceleration techniques for iterative methods for linear systems of both static (Qy = b) and dynamic (y′ = Qy + g(t)) type are analyzed. A new splitting Q = M - N, where M is block-Toeplitz is proposed. In the static case considerable improvement is observed, while in the dynamic case this preconditioning results only in a slightly faster waveform relaxation scheme than the traditional block-Jacobi dynamic iteration method in the case of linear systems approximating heat equation in one or two dimensions. It is shown that the static analysis does not predict correctly the optimal value of the parameters introduced for the dynamic case, but that a spectral analysis does.
AB - Acceleration techniques for iterative methods for linear systems of both static (Qy = b) and dynamic (y′ = Qy + g(t)) type are analyzed. A new splitting Q = M - N, where M is block-Toeplitz is proposed. In the static case considerable improvement is observed, while in the dynamic case this preconditioning results only in a slightly faster waveform relaxation scheme than the traditional block-Jacobi dynamic iteration method in the case of linear systems approximating heat equation in one or two dimensions. It is shown that the static analysis does not predict correctly the optimal value of the parameters introduced for the dynamic case, but that a spectral analysis does.
KW - Accelerating of convergence
KW - Iterative methods
KW - Overlapping
KW - Preconditioning
KW - Splitting
KW - Waveform relaxation method
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UR - http://www.scopus.com/inward/citedby.url?scp=0041375925&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0041375925
VL - 279
SP - 51
EP - 74
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
SN - 0024-3795
IS - 1-3
ER -