Numerical stability of nested dissection orderings
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- by Indu Mati Anand PDF
- Math. Comp. 35 (1980), 1235-1249 Request permission
Abstract:
Rigorous bounds on rounding errors for sparse positive definite matrices are obtained. When used for nested dissection orderings of finite element matrices, the analysis furnishes bounds which are stronger than those for band orderings.References
- Indu Mati Anand, Numerical stability of nested dissection orderings, Math. Comp. 35 (1980), no.ย 152, 1235โ1249. MR 583501, DOI 10.1090/S0025-5718-1980-0583501-0
- Garrett Birkhoff and Alan George, Elimination by nested dissection, Complexity of sequential and parallel numerical algorithms (Proc. Sympos., Carnegie-Mellon Univ., Pittsburgh, Pa., 1973) Academic Press, New York, 1973, pp.ย 221โ269. MR 0366010
- I. S. Duff, A. M. Erisman, and J. K. Reid, On Georgeโs nested dissection method, SIAM J. Numer. Anal. 13 (1976), no.ย 5, 686โ695. MR 426396, DOI 10.1137/0713056
- George E. Forsythe and Cleve B. Moler, Computer solution of linear algebraic systems, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219223 A. GEORGE, An Efficient Band Oriented Scheme for Solving $n \times n$ Grid Problems, Proc. Fall Joint Computer Conference, 1972.
- Alan George, Nested dissection of a regular finite element mesh, SIAM J. Numer. Anal. 10 (1973), 345โ363. MR 388756, DOI 10.1137/0710032
- Alan George, Numerical experiments using dissection methods to solve $n$ by $n$ grid problems, SIAM J. Numer. Anal. 14 (1977), no.ย 2, 161โ179. MR 440882, DOI 10.1137/0714011
- J. Alan George, Solution of linear systems of equations: direct methods for finite element problems, Sparse matrix techniques (Adv. Course, Technical Univ. Denmark, Copenhagen, 1976) Lecture Notes in Math., Vol. 572, Springer, Berlin, 1977, pp.ย 52โ101. MR 0440883
- Alan George and Joseph W. H. Liu, An automatic nested dissection algorithm for irregular finite element problems, SIAM J. Numer. Anal. 15 (1978), no.ย 5, 1053โ1069. MR 507564, DOI 10.1137/0715069
- Alan George, William G. Poole Jr., and Robert G. Voigt, Incomplete nested dissection for solving $n$ by $n$ grid problems, SIAM J. Numer. Anal. 15 (1978), no.ย 4, 662โ673. MR 474729, DOI 10.1137/0715044
- Alan J. Hoffman, Michael S. Martin, and Donald J. Rose, Complexity bounds for regular finite difference and finite element grids, SIAM J. Numer. Anal. 10 (1973), 364โ369. MR 347065, DOI 10.1137/0710033
- Richard J. Lipton, Donald J. Rose, and Robert Endre Tarjan, Generalized nested dissection, SIAM J. Numer. Anal. 16 (1979), no.ย 2, 346โ358. MR 526496, DOI 10.1137/0716027
- J. K. Reid, A note on the stability of Gaussian elimination, J. Inst. Math. Appl. 8 (1971), 374โ375. MR 298861 O. WIDLUND, "On the use of sparsity of finite element systems of equations by Gaussian elimination-type methods," Actas del Seminario Sobre Metodos Numericos Modernas, Vol. 2, Universidad Central de Venezuela, 1974.
- J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422
- J. H. Wilkinson, A priori error analysis of algebraic processes, Proc. Internat. Congr. Math. (Moscow, 1966) Izdat. โMirโ, Moscow, 1968, pp.ย 629โ640. MR 0233532
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Math. Comp. 35 (1980), 1235-1249
- MSC: Primary 65F05; Secondary 65N20
- DOI: https://doi.org/10.1090/S0025-5718-1980-0583501-0
- MathSciNet review: 583501