27
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Sor method and p-cyclic matrices (I)

&
Pages 57-76 | Received 15 Dec 1989, Published online: 19 Mar 2007

References

  • Ehrlich , L. W. 1972 . Coupled harmonic equations, SOR and Chebyshev acceleration . Math Comp , 26 : 335 – 343 .
  • Evans , D. J. and Li , C. 1989 . A note on the SOR and CG methods for the large sparse least squares problems . Linear Algebra Appl , 121 : 163 – 170 .
  • Evans D. J. Li C. Successive underrelaxation (SUR) method for the hyperbolic initial boundary value problem in preparation
  • Galanis , G. , Hadjidimos , A. and Noutsos , D. 1988 . On the convergence of mono-parametric k-step iterative Euler methods for the solution of linear systems . Int. J. Comp. Math. , 26 : 45 – 56 .
  • Galanis , S. , Hadjidimos , A. and Noutsos , D. 1988 . On the equivalence of the k-step iterative Euler methods and successive overrelaxation (SOR) method for k-cyclic matrices . Math. Comput. Sim. , 30 : 213 – 230 .
  • Galanis , S. , Hadjidimos , A. and Noutsos , D. On the relationship between the Jacobi and the successive overrelaxation (SOR) matrices of the k-cyclic matrices . Comp. and Math, with Appl. , to appear.
  • Li C. Iterative methods for a class of large, sparse, non-symmetric linear systems Dept. of Computer Studies, Loughborough University of Technology U. K. 1989 Ph.D. Thesis
  • Markham , T. L. , Neumann , M. and Plemmons , R. J. 1985 . Convergence of a direct-iterative method for large scale least squares problems . Linear Algebra Appl , 69 : 155 – 167 .
  • Niethammer , W. 1964 . Relaxation bei Matrizen mit der Eigenschaft “A” . Z. Angew. Math. Mech. , 44 : T49 – T52 .
  • Niethammer , W. , Pillis , J. de and Varga , R. S. 1984 . Convergence of block iterative methods applied to sparse least-squares problems . Lin. Alg. Appl. , 58 : 327 – 341 .
  • Pierce D. J. Parallel least squares computations and related matrices N. C. State Univ. Raleigh, N. C. Ph.D. Thesis
  • Rivlin , J. Th. 1974 . The Chebyshev Polynomials , New York : Wiley .
  • Tee , G. J. 1964 . An application of p-cyclic matrices for solving periodic parabolic problems . Num. Math. , 6 : 162 – 189 .
  • Varga , R. S. 1959 . p-cyclic matrices: A generalization of Young-Frankel successive overrelaxation scheme . Pac. J. of Maths. , 9 : 617 – 628 .
  • Varga , R. S. 1962 . Matrix Iterative Analysis , Englewood Cliffs : Prentice-Hall .
  • Wild , P. and Niethammer , W. 1987 . Over and underrelaxation for linear systems with weakly cyclic Jacobi matrices of index of p . Lin. Alg. Appl. , 91 : 29 – 52 .
  • Young , D. M. 1954 . Iterative methods for solving partial difference equations of elliptic type . Trans. Amer. Math. Soc. , 76 : 92 – 111 .
  • Young , D. M. 1971 . Iterative Solutions of Large Linear Systems , New York : Academic Press .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.