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International Journal of Computer Mathematics Volume 88, 2011 - Issue 1
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Section A

Chebyshev polynomial acceleration for block SOR methods for solving the rank-deficient least-squares problem

Bing Zheng Department of Mathematics, Lanzhou University, Lanzhou, 730000, China
,
Liying Duan Department of Mathematics, Lanzhou University, Lanzhou, 730000, ChinaView further author information
&
Ke Wang Department of Mathematics, College of Sciences, Shanghai University, Shanghai, 200444, ChinaCorrespondence[email protected]
Pages 6-20 | Received 19 Feb 2008, Accepted 25 Oct 2009, Published online: 02 Dec 2010

References

  • Berman , A. and Plemmons , R. J. 1974 . Cones and iterative methods for best least squares solutions of linear systems . SIAM J. Numer. Anal. , 11 : 145 – 154 .
  • Chen , Y. T. 1975 . “ Iterative methods for linear least squares problems ” . ON, Canada : University of Waterloo . Doctoral Thesis
  • Darvishi , M. T. , Khani , F. , Hamedi-nezhad , S. and Zheng , B. 2008 . Symmetric block-SOR methods for rank-deficient least squares problems . J. Comput. Appl. Math. , 215 : 14 – 27 .
  • Hageman , L. A. and Young , D. M. 1981 . Applied Iterative Methods , 20 – 59 . New York : Academic Press .
  • Manteuffel , T. A. 1977 . The Tchebychev iteration for nonsymmetric linear systems . Numer. Math. , 28 : 307 – 327 .
  • Markham , T. L. , Neumann , M. and Plemmons , R. J. 1985 . Convergence of a direct-iterative method for large-scale leasr-squares problems . Linear Algebr. Appl. , 69 : 155 – 167 .
  • Miller , V. A. and Neumann , M. 1987 . Successive overrelaxation methods for solving the rank deficient linear least squares problem . Linear Algebr. Appl. , 88/89 : 533 – 557 .
  • Niethammer , W. , de Pillis , J. and Varga , R. S. 1985 . Convergence of block iterative methods applied to sparse least squares problems . Linear Algebr. Appl. , 58 : 327 – 341 .
  • Rashidinia , J. and Jafarzadeh , E. 2007 . Accelerated generalized successive overrelaxation method for least squares problems . Appl. Math. Comput. , 186 : 175 – 183 .
  • Santos , C. H. , Silva , B. P.B. and Yuan , J. Y. 1998 . Block SOR methods for rank-deficient least-squares problems . J. Comput. Appl. Math. , 100 : 1 – 9 .
  • Tian , H. 2003 . Accelerate overrelaxation methods for rank deficient linear systems . Appl. Math. Comput. , 140 : 485 – 499 .
  • Young , D. M. 1971 . Iterative Solution of Large Linear Systems , New York : Academic Press .
  • Yuan , J. Y. , de Sampaio , R. J.B. and Sun , W. 1996 . Algebraic relationships between updating and downdating least-squares problems . Numer. Math. J. Chinese Univ. , 3 : 203 – 210 . (in Chinese)
  • Zheng , B. and Wang , K. 2005 . Symmetric successive overrelaxation methods for solving the rank deficient linear least squares problem . Appl. Math. Comput. , 169 : 1305 – 1323 .

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