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November 2007 Splitting iteration methods for non-Hermitian positive definite systems of linear equations
Zhong-Zhi BAI
Hokkaido Math. J. 36(4): 801-814 (November 2007). DOI: 10.14492/hokmj/1272848034


For large sparse system of linear equations with a non-Hermitian positive definite coefficient matrix, we review the recently developed Hermitian/skew-Hermitian splitting (HSS) iteration, normal/skew-Hermitian splitting (NSS) iteration, positive-definite/skew-Hermitian splitting (PSS) iteration, and block triangular/skew-Hermitian splitting (BTSS) iteration. These methods converge unconditionally to the exact solution of the linear system, with the upper bounds of their convergence factors being only dependent on the spectrum of the Hermitian (or normal, or positive-definite) splitting matrix, but independent of the spectrum of the skew-Hermitian splitting matrix as well as the eigenvectors of all matrices involved.


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Zhong-Zhi BAI. "Splitting iteration methods for non-Hermitian positive definite systems of linear equations." Hokkaido Math. J. 36 (4) 801 - 814, November 2007.


Published: November 2007
First available in Project Euclid: 3 May 2010

zbMATH: 1138.65027
MathSciNet: MR2378292
Digital Object Identifier: 10.14492/hokmj/1272848034

Primary: 65F50
Secondary: 65F10, 65F15

Rights: Copyright © 2007 Hokkaido University, Department of Mathematics


Vol.36 • No. 4 • November 2007
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