Preconditioned conjugate gradient methods applied to certain symmetric linear systems

References

• Agarwal , R. K. 1983 . “ A fourth-order compact scheme for the Helmholtz equation in curvilinear coordinates ” . In Scientific Computing , Edited by: Stepleman , R. S. 147 – 154 . North-Holland Publishing Co .
   Google Scholar
• Axelsson , O. 1974 . “ On preconditioning and convergence acceleration in sparse matrix problems ” . In CERN 74-10 Geneva
   Google Scholar
• Axelsson , O. and Barker , V. A. 1984 . Finite Elements Solution of Boundary Value Problems: Theory and Computation , Academic Press .
   Google Scholar
• Collatz , L. 1966 . The Numerical Treatment of Differential Equations , NY : Springer-Verlag .
   Google Scholar
• Evans , D. J. 1967 . The use of preconditioning in iterative methods for solving linear equation with symmetric positive definite matrices . J. Inst. Maths. Applics. , 4 : 295 – 314 .
   Google Scholar
• Evans , D. J. 1983 . Preconditioning Methods: Analysis and Applications , NY : Gordon and Breach Science Publishers .
   Google Scholar
• Gottlieb , D. and Orszag , S. A. . Numerical Analysis of Spectral Methods: Theory and Applications . CBMS Regional Conference Series in Applied Mathematics . Vol. 269 , SIAM .
   Google Scholar
• Gustafsson , I. 1978 . A class of first order factorization methods . BIT , 18 : 142 – 156 .
   Google Scholar
• Hestenes , M. R. and Steifel , E. 1952 . Method of conjugate gradients for solving linear systems . J. Res. Nat. Bur. Stand , 49 : 409 – 436 .
   Google Scholar
• Hirsh , R. S. 1983 . High order approximations in fluid mechanics—compact to spectral . Von Karman Institute for Fluid Dynamics Series , 4
   Google Scholar
• Hoskins , B. J. 1982 . “ Spectral methods in meteorology ” . In Numerical Methods for Fluid Dynamics , Edited by: Morton , K. W. and Baines , M. J. 45 – 62 . Academic Press .
   Google Scholar
• Lynch , R. E. and Rice , J. R. 1978 . “ The hodie method and its performance for solving elliptic partial differential equations ” . In Recent Advances in Numerical Analysis , Edited by: De Boor , C. and Golub , G. H. 143 – 176 . Academic Press .
   Google Scholar
• Manohar , R. and Stephenson , J. W. 1982 . Optimal finite analytic methods . J. Heat Transfer , 104 : 432 – 437 .
   Google Scholar
• Meijerink , J. A. and van der Vorst , H. A. 1977 . An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix . Math. Comp. , 31 : 148 – 162 .
   Web of Science ®Google Scholar
• Wong Y. S. Iterative Methods for Problems in Numerical Analysis D. Phil. Thesis Oxford University 1978
   Google Scholar
• Wong Y. S. Preconditioned gradient type methods applied to certain non-symmetric linear systems 1986 (in preparation)
   Google Scholar
• Wong Y. S. Iterative methods for the solution of elliptic difference equations on Cyber 205 computers 1986 (in preparation)
   Google Scholar