References
Arms, R. J., L. D. Gates andB. Zondek: A method of block iteration. Journal Soc. Indust. Appl. Math.4, 220–229 (1956).
Blair, A., N. Metropolis, J. v. Neumann, A. H. Taub andM. Tsingou: A study of a numerical solution of a two-dimensional hydrodynamical problem. Math. Tables and Other Aids to Computation13, 145–184 (1959).
Cuthill, Elizabeth H., andRichard S. Varga: A method of normalized block iteration. Journal Assoc. Computing Mach.6, 236–244 (1959).
Flanders, Donald A., andGeorge Shortley: Numerical determination of fundamental modes. Journal of Applied Physics21, 1326–1332 (1950).
Forsythe, G. E.: Solving linear algebraic equations can be interesting. Bull. Amer. Math. Soc.59, 299–329 (1953).
Frank, Werner: Solution of linear systems byRichardson's method. Journal Assoc. Computing Mach.7, 274–286 (1960).
Frankel, Stanley P.: Convergence rates of iterative treatments of partial differential equations. Math. Tables Aids Comput.4, 65–75 (1950).
Golub, Gene H.: The use of Chebyshev matrix polynomials in the iterative solution of linear equations compared with the method of successive overrelaxation. Doctoral Thesis, University of Illinois, 1959.
Heller, J.: Simultaneous, successive and alternating direction iterative methods. Journal Soc. Indust. Appl. Math.8, 150–173 (1960).
Householder, A. S.: The approximate solution of matrix problems. Journal Assoc. Computing Mach.5, 205–243 (1958).
Kahan, W.: Gauss-Seidel methods of solving large systems of linear equations. Doctoral Thesis, University of Toronto, 1958.
Lanczos, Cornelius: Solution of systems of linear equations by minimized iterations. Journal Research Nat. Bureau of Standards49, 33–53 (1952).
Parter, Seymour V.: On two-line iterative methods for the Laplace and biharmonic difference equations. Numerische Mathematik1, 240–252 (1959).
Riley, James D.: Iteration procedures for the dirichlet Difference problem. Math. Tables Aids Comput.8, 125–131 (1954).
Romanovsky, V.: Recherches sur les chaînes deMarkoff. Acta Math.66, 147–251 (1936).
Sheldon, J. W.: On the spectral norms of several iterative processes. Journal Assoc. Computing Mach.6, 494–505 (1959).
Stiefel, Eduard L.: Kernel polynomials in linear algebra and their numerical applications. National Bureau of Standards Applied Math. Series 49, U.S. Government Printing Office, Washington, D. C. 1958, p. 1–22.
Todd, John: The condition of a certain matrix. Proc. Cambridge Philos. Soc.46, 116–118 (1950).
Varga, Richard S.: A comparison of the successive overrelaxation method and semi-iterative methods using Chebyshev polynomials. Journal Soc. Indust. Appl. Math.5, 39–46 (1957).
Varga, Richard S.: Numerical solution of the two-group diffusion equation inx−y geometry. IRE Trans. of the Professonal Group on Nuclear Science, N.S.4, 52–62 (1957).
Varga, Richard S.:p-cyclic matrices: a generalization of the Young-Frankel successive overrelaxation scheme. Pacific Journal of Math.9, 617–628 (1959).
Varga, Richard S.: Factorization and normalized iterative methods. Boundary Problems in Differential Equations, the University of Wisconsin Press, Madison 1960, p. 121–142.
Wachspressm E. L., P. M. Stone andC. E. Lee: Mathematical techniques in two-space-dimension multigroup calculations. Proceedings of the Second United Nations International Conference on the Peaceful Uses of Atomic Energy, United Nations, Geneva, 1958, volume 16, p. 483–488.
Wielandt, Helmut: Unzerlegbare, nicht negative Matrizen. Math. Z.52, 642–648 (1950).
Young, David: Iterative methods for solving partial differences equations of elliptic type. Doctoral Thesis, Harvard University, 1950.
Young, David: OnRichardson's method for solving linear systems with positive definite matrices. Journal Math. and Physics32, 243–255 (1953).
Young, David: Iterative methods for solving partial difference equations of elliptic type. Trans. Amer. Math. Soc.76, 92–111 (1954).
Young, David: On the solution of linear systems by iteration. Proceedings of the Sixth Symposium in Applied Math., p. 283–298. New York: McGraw-Hill 1956.
Author information
Authors and Affiliations
Additional information
This paper includes work from the doctoral dissertation [7] of the first author, who wishes to thank ProfessorA. H. Taub of the University of Illinois for guidance and encouragement in the preparation of that dissertation.
Rights and permissions
About this article
Cite this article
Golub, G.H., Varga, R.S. Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods. Numer. Math. 3, 147–156 (1961). https://doi.org/10.1007/BF01386013
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01386013