On sparse and compact preconditioned conjugate gradient methods for partial differential equations

References

• Evans , D.J. 1963 . The extrapolated modified Aitken iteration method for solving elliptic difference equations . Comp.J , 6 : 193 – 201 .
   Google Scholar
• Evans , D.J. 1968 . The use of preconditioning in iterative methods for solving linear equations with symmetric positive definite matrices . J.I.M.A , 4 : 295 – 314 .
   Google Scholar
• Evans , . 1973 . Comparison of the convergence rates of iterative methods for solving linear equations with preconditioning . Greek Math. Soc, Carathéodory Symp . 1973 . pp. 106 – 135 .
   Google Scholar
• Evans , D.J. and Missirlis , N.M. 1979 . The modified alternating direction preconditioning method for the numerical solution of elliptic self-adjoint partial differential equations . B.I.T , 19 : 172 – 185 .
   Google Scholar
• Forsythe , G.E. and Wasow , W.R. 1960 . Finite Difference Methods for Partial Differential Equations , New York : John Wiley & Sons .
   Google Scholar
• Niethammer . 1964 . Relaxation bei Komplexen mairizen . Math. Zeii , 86 : 34 – 40 .
   Google Scholar
• Missirlis , N.M. 1978 . Preconditioned Iterative Methods for Solving Elliptic Partial Differential Equations , Loughborough : University of Technology . Ph.D. Thesis
   Google Scholar
• Varga , R.S. 1962 . Matrix Iterative Analysis , Englewood Cliffs, New Jersey : Prentice-Hall .
   Google Scholar
• Young , D.M. 1971 . Iterative Solution of Large Systems , London, New York : Academic Press .
   Google Scholar
• Stone , H.L. 1968 . Iterative solution of implicit approximations of multi-dimensional partial differential equations . SIAM J. Numer. Anal , 5 : 530 – 558 .
   Web of Science ®Google Scholar
• Dupont , T. , Kendall , R. and Rachford , H.H. Jr . 1968 . An approximate factorisation procedure for solving self-adjoint elliptic difference equations . SIAM J. Numer. Anal , 5 : 559 – 573 .
   Web of Science ®Google Scholar
• Meijerink , J.A. and Van Der Vorst , H.A. 1977 . An iterative solution method of linear systems of which the coefficient matrix is asymmetric M-matrix . Math. of Camp , 31 : 148 – 162 .
   Web of Science ®Google Scholar
• David , S.Kershaw. 1978 . The incomplete Cholesky-Conjugate Gradient Method for the iterative solution of systems of linear equations . Jour. Comp. Phys , 26 : 43 – 65 .
   Google Scholar
• Young , D.M. 1977 . On the accelerated SSOR method for solving large linear systems . Adv. in Math , 23 : 215 – 271 .
   Web of Science ®Google Scholar
• Gustafsson , I. 1978 . A class of first order factorization methods . BIT , 18 : 142 – 156 .
   Google Scholar
• Lipitakis , E.A. and Evans , D.J. 1979 . “ A sparse LU factorization procedure for the solution of parabolic differential equations ” . In Numerical Methods in Thermal Problems , Edited by: Lewis , R.W. and Morgan . Swansea, , U.K : Pineridge Press .
   Google Scholar
• Evans , D.J. and Lipitakis , E.A. 1980 . A normalised implicit conjugate gradient method for the solution of large sparse systems of linear equations . Comp. Meth. in Appl. Mech. Eng , 23 : 1 – 19 .
   Google Scholar
• Cuthill , E.H. and Varga , R.S. 1959 . A method of normalized block iteration . J.A.C.M , 6 : 236 – 244 .
   Google Scholar
• Benson , A. and Evans , D.J. 1979 . A normalized algorithm for the solution of symmetric general five-term linear systems of semi-bandwidth m . Jour. Comp. and Appl. Maths , 5 : 299 – 304 .
   Google Scholar
• Lipitakis , E.A. 1978 . Computational and Algorithmic Techniques for the Solution of Elliptic and Parabolic P.D.E.'s in Two and Three Space Dimensions , Loughborough : University of Technology . Ph.D. Thesis
   Google Scholar
• Evans , D.J. 1973 . The analysis and application of sparse matrix algorithms in the finite element method . The Mathematics of Finite Elements and Applications Procs . 1973 . Edited by: Whiteman , J. pp. 427 – 447 . London : Acad. Press . presented at Mafelap Conference. April 1972
   Google Scholar
• Young D M. Notes on the Conjugate Gradient Method 1975 unpub
   Google Scholar
• Chandra R. Eisenstat S. C. Schultz M. H. Conjugate gradient methods for partial differential equations Adv. in Comp. Meth. for P.D.E's A.I.C.A. 1975 60 64
   Google Scholar
• Ehrlich , L.W. 1963 . The Block Symmetric Successive Overrelaxation Metho , Austin : University of Texas . Ph.D. Thesis
   Google Scholar
• Varga , R.S. 1960 . “ Factorisation and normalised iterative methods ” . In Boundary Problems in Differential Equations , Edited by: Langer , R.E. Madison, Wisconsin : University Wisconsin Press .
   Google Scholar
• Hestenes , M.R. and Stiefel . 1952 . Methods of conjugate gradients for solving linear systems . NBS, J. of Res , 49 : 409 – 436 .
   Google Scholar