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International Journal of Computer Mathematics Volume 84, 2007 - Issue 11: Celebrating the Life of David J. Evans
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Original Articles

An iterative method for positive real systems

M. M. Martins Department of Mathematics, University of Coimbra, 3000, Coimbra, PortugalCorrespondence[email protected]
,
M. E. Trigo High Account and Administration Institute of Coimbra, 3000, Coimbra, Portugal
&
D. J. Evans Parallel Computer Center, University of Loughborough, Leicestershire, UK
Pages 1603-1611 | Received 19 Nov 2005, Accepted 08 Oct 2006, Published online: 18 Oct 2007

References

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  • Young , D. M. 1971 . Iterative Solution of Large Linear Systems , New York and London : Academic Press .
  • Hadjidimos , A. 1978 . Accelerated overrelaxation method . Mathematics of Computation , 32 : 149 – 157 .
  • Hadjidimos , A. , Psimarni , A. and Yeyios , A. K. 1992 . On the convergence of the modified accelerated overrelaxation (MAOR) method . Applied Numerical Mathematics , 10 : 115 – 127 .
  • Martins , M. M. and Trigo , M. E. 1994 . On the convergence of the interval (MAOR) method . Applied Numerical Mathematics , 15 : 439 – 448 .
  • Neumaier , A. 1984 . New techniques for the analyses of linear interval equations . Linear Algebra and its Applications , 58 : 273 – 325 .
  • Li , C. , Liang , X. and Evans , D. J. 2001 . An iterative method for the positive real linear system . International Journal of Computer Mathematics , 78 : 153 – 163 .
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  • Jia-gan , H. 1982 . Estimates of ‖B− 1 A‖∞ their applications . Mathematical and Numerical Sin , 4 : 272 – 282 .
  • Jia-gan , H. 1980 . Upper bounds of the spectral radius of some iterative methods . Journal of Computer Mathematics , 8 : 118 – 127 .
  • Xinmin , W. and Evans , D. J. 1994 . The upper bound of the spectral radius of M− 1N and the convergence of some iterative methods . International Journal of Computer Mathematics , 53 : 203 – 217 .
  • Martins , M. M. 1991 . “ On the generalized iterative method for linear systems with matrices belonging to the class C1 ” . In Numerical Methods, Colloquia Mathematica Societatis. János Bolyai , Edited by: Greenspan , D. and Rósza , P. Vol. 59 , 29 – 36 . Amsterdam, , The Netherlands : Elsevier Science .
  • Qingrong , L. and Zhiying , J. 1987 . The SOR method for solving linear interval equations . Freiburger Interval Berichte , 87 ( 7 ) : 1 – 7 .
  • Cvetković , L. and Herceg , D. 1989 . The AOR method for solving linear interval equations . Computing , 41 : 359 – 364 .
  • Evans , D. J. and Martins , M. M. 1992 . On the convergence of some extrapolated methods . Proceedings of International Symposium on Numerical Analysis , Praga
  • Martins , M. M. 1988 . Extended convergence regions for the AOR method . Journal of Computation and Applied Mathematics , 24 : 327 – 336 .

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