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International Journal of Computer Mathematics Volume 84, 2007 - Issue 8: Fast Iterative and Preconditioning Methods for Linear and Non–Linear Systems
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A short note on singular values of optimal and superoptimal preconditioned matrices

Xiao-Qing Jin Department of Mathematics, University of Macau, Macao, P.R. China
&
Yi-Min Wei Institute of Mathematics, School of Mathematical Sciences, Fudan University, Shanghai, 200433, P.R. China; Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education, P.R. ChinaCorrespondence[email protected]
Pages 1261-1263 | Received 09 Mar 2007, Accepted 14 Mar 2007, Published online: 28 Aug 2007

References

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  • Jin , X. and Wei , Y. 2007 . A survey and some extensions of T. Chan's preconditioner . Linear Algebra and its Applications , to appear
  • Di Benedetto , F. and Serra , S. 2000 . Optimal mutilevel matrix algebra operators . Linear and Multilinear Algebra , 4 : 35 – 66 .
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  • Chan , R. and Jin , X. 2007 . An Introduction to Iterative Toeplitz Solvers , Philadelphia : SIAM .
  • Chan , R. , Jin , X. and Yeung , M. 1991 . The circulant operator in the Banach algebra of matrices . Linear Algebra and its Applications , 149 : 41 – 53 .
  • Di Benedetto , F. and Serra , S. 2002 . A Note on superoptimal matrix algebra operators . Linear and Multilinear Algebra , 50 : 343 – 372 .
  • Cheng , C. , Jin , X. , Vong , S. and Wang , W. 2007 . A note on spectra of optimal and superoptimal preconditioned matrices . Linear Algebra and its Applications , 422 : 482 – 485 .
  • Horn , R. and Johnson , C. 1985 . Matrix Analysis , Cambridge : Cambridge University Press .
  • Di Benedetto , F. , Estatico , C. and Serra , S. 2005 . Superoptimal preconditioned conjugate gradient iteration for image deblurring . SIAM Journal on Scientific Computing , 26 : 1012 – 1035 .

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