P-CYCLIC MATRICES: A GENERALIZATION OF THE YOUNG-FRANKEL SUCCESSIVE OVERRELAXATION SCHEME
The Young-Frankel successive overrelaxation scheme, which was shown to be applicable in the numerical solution of self-adjoint partial diffcrential equations of elliptic type, is described. Successive overrelaxation is a theory which depends on what Young calls (point) property (Al. Both point and block property (A) can be interpreted via the works of Romanovsky and Frobenius on finite Markoff chains and stochastic matrices. It is shown that the fundamental lemma of the theory of successive overrelaxation follows as a corollary to a theorem by Romanovsky on cyclic matrices, which in turn leads to a generalization of both point and block property (A). It is also shown that the results previously obtained apply to the solution of Laplace's equation on a uniform triangular mesh. (M.H.R.)
- Research Organization:
- Westinghouse Electric Corp. Bettis Plant, Pittsburgh
- DOE Contract Number:
- AT(11-1)-GEN-14
- NSA Number:
- NSA-12-003043
- OSTI ID:
- 4317093
- Report Number(s):
- WAPD-T-567
- Country of Publication:
- United States
- Language:
- English
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