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Original Articles

The use of preconditioning in direct methods of solving positive definite linear systems

Pages 101-121 | Received 30 Sep 1997, Published online: 30 Mar 2007

References

  • Hatzopoulos M. Preconditioning and other computational Techniques for Direct solution of Linear Equations Ph.D. Theses, Loughbrough university. 1974
  • Bauer , F. L. 1963 . Optimally Scaled Matrices . Num. Math. , 5 : 73 – 87 .
  • Evans , D. J. 1968 . The use of Preconditioning in Iterative Methods for soving linear Equations with symmetric positive definte Matrices . J.I.M.A. , 4 : 295 – 314 .
  • Hatzopoulos , M. and Evans , D. J. 1977 . On the Direct Solution of Preconditioned Linear Equations . Bull. Greek. Math. Soc. , 16 : 30 – 44 .
  • Turing , A. M. 1948 . Rounding Errors in Matrix Processes . Quart. J. Mech. and App. Machs. , 1 : 287 – 308 .
  • Von Neumann , J. and Goldstine , H. H. 1947 . Numerical inverting of Matrixes of High order . Bull. Amer. Math. Soc. , 53 : 1021 – 1099 .
  • Davis , P. , Haynsworth , E. V. and Marcus , M. 1961 . Bounds for the P-condition number of Matrixes with postive roots . Jour. Res. N.B.S. , 65B
  • Todd , J. 1954 . The condition of the Finite Segments of the Hilbert matrix . N.B.S. AMS. , 39 : 109 – 116 .

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