Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods. I, II. (English) Zbl 0099.10903
Keywords:
numerical analysisReferences:
| [1] | Arms, R. J., L. D. Gates andB. Zondek: A method of block iteration. Journal Soc. Indust. Appl. Math.4, 220?229 (1956). · Zbl 0077.32502 · doi:10.1137/0104012 |
| [2] | 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). · Zbl 0102.33603 · doi:10.2307/2002710 |
| [3] | Cuthill, Elizabeth H., andRichard S. Varga: A method of normalized block iteration. Journal Assoc. Computing Mach.6, 236?244 (1959). · Zbl 0088.09403 · doi:10.1145/320964.320981 |
| [4] | Flanders, Donald A., andGeorge Shortley: Numerical determination of fundamental modes. Journal of Applied Physics21, 1326?1332 (1950). · Zbl 0039.34101 · doi:10.1063/1.1699598 |
| [5] | Forsythe, G. E.: Solving linear algebraic equations can be interesting. Bull. Amer. Math. Soc.59, 299?329 (1953). · Zbl 0052.12903 · doi:10.1090/S0002-9904-1953-09718-X |
| [6] | Frank, Werner: Solution of linear systems byRichardson’s method. Journal Assoc. Computing Mach.7, 274?286 (1960). · Zbl 0097.11404 · doi:10.1145/321033.321041 |
| [7] | Frankel, Stanley P.: Convergence rates of iterative treatments of partial differential equations. Math. Tables Aids Comput.4, 65?75 (1950). · doi:10.2307/2002770 |
| [8] | 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. |
| [9] | Heller, J.: Simultaneous, successive and alternating direction iterative methods. Journal Soc. Indust. Appl. Math.8, 150?173 (1960). · Zbl 0109.34602 · doi:10.1137/0108009 |
| [10] | Householder, A. S.: The approximate solution of matrix problems. Journal Assoc. Computing Mach.5, 205?243 (1958). · Zbl 0094.31003 · doi:10.1145/320932.320933 |
| [11] | Kahan, W.: Gauss-Seidel methods of solving large systems of linear equations. Doctoral Thesis, University of Toronto, 1958. |
| [12] | Lanczos, Cornelius: Solution of systems of linear equations by minimized iterations. Journal Research Nat. Bureau of Standards49, 33?53 (1952). · doi:10.6028/jres.049.006 |
| [13] | Parter, Seymour V.: On two-line iterative methods for the Laplace and biharmonic difference equations. Numerische Mathematik1, 240?252 (1959). · Zbl 0094.31201 · doi:10.1007/BF01386388 |
| [14] | Riley, James D.: Iteration procedures for the dirichlet Difference problem. Math. Tables Aids Comput.8, 125?131 (1954). · Zbl 0055.35604 · doi:10.2307/2001924 |
| [15] | Romanovsky, V.: Recherches sur les chaînes deMarkoff. Acta Math.66, 147?251 (1936). · Zbl 0014.02802 · doi:10.1007/BF02546519 |
| [16] | Sheldon, J. W.: On the spectral norms of several iterative processes. Journal Assoc. Computing Mach.6, 494?505 (1959). · Zbl 0168.13502 · doi:10.1145/320998.321003 |
| [17] | 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. · Zbl 0171.35703 |
| [18] | Todd, John: The condition of a certain matrix. Proc. Cambridge Philos. Soc.46, 116?118 (1950). · Zbl 0034.37601 · doi:10.1017/S0305004100025536 |
| [19] | 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). · Zbl 0080.10701 · doi:10.1137/0105004 |
| [20] | 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). · doi:10.1109/TNS2.1957.4315586 |
| [21] | Varga, Richard S.:p-cyclic matrices: a generalization of the Young-Frankel successive overrelaxation scheme. Pacific Journal of Math.9, 617?628 (1959). · Zbl 0088.09402 · doi:10.2140/pjm.1959.9.617 |
| [22] | Varga, Richard S.: Factorization and normalized iterative methods. Boundary Problems in Differential Equations, the University of Wisconsin Press, Madison 1960, p. 121?142. |
| [23] | 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. |
| [24] | Wielandt, Helmut: Unzerlegbare, nicht negative Matrizen. Math. Z.52, 642?648 (1950). · Zbl 0035.29101 · doi:10.1007/BF02230720 |
| [25] | Young, David: Iterative methods for solving partial differences equations of elliptic type. Doctoral Thesis, Harvard University, 1950. |
| [26] | Young, David: OnRichardson’s method for solving linear systems with positive definite matrices. Journal Math. and Physics32, 243?255 (1953). |
| [27] | Young, David: Iterative methods for solving partial difference equations of elliptic type. Trans. Amer. Math. Soc.76, 92?111 (1954). · Zbl 0055.35704 · doi:10.1090/S0002-9947-1954-0059635-7 |
| [28] | 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. · Zbl 0071.11801 |
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