Geodesic
Elimination on sparse symmetric systems of a special structure
Applications of Mathematics, Tome 17 (1972) no. 6, pp. 448-460
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The problem of solving sparse symmetric linear algebraic systems by elimination is discussed. A brief survey of the techniques used is given. Another approach is introduced in the paper. It is more general than the band matrix approach. However, the matrix is not treated element by element as in the most general approach. The procedure for finding the ordering of rows and columns of a matrix suitable for the considered modification of elimination is given. The examples of matrices reordered by the proposed procedure are shown.
The problem of solving sparse symmetric linear algebraic systems by elimination is discussed. A brief survey of the techniques used is given. Another approach is introduced in the paper. It is more general than the band matrix approach. However, the matrix is not treated element by element as in the most general approach. The procedure for finding the ordering of rows and columns of a matrix suitable for the considered modification of elimination is given. The examples of matrices reordered by the proposed procedure are shown.
DOI : 10.21136/AM.1972.103436
Classification : 15A06, 34-xx, 65F05 
@article{10_21136_AM_1972_103436,
     author = {Segethov\'a, Jitka},
     title = {Elimination on sparse symmetric systems of a special structure},
     journal = {Applications of Mathematics},
     pages = {448--460},
     year = {1972},
     volume = {17},
     number = {6},
     doi = {10.21136/AM.1972.103436},
     mrnumber = {0312706},
     zbl = {0259.65035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1972.103436/}
}
TY  - JOUR
AU  - Segethová, Jitka
TI  - Elimination on sparse symmetric systems of a special structure
JO  - Applications of Mathematics
PY  - 1972
SP  - 448
EP  - 460
VL  - 17
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1972.103436/
DO  - 10.21136/AM.1972.103436
LA  - en
ID  - 10_21136_AM_1972_103436
ER  - 
%0 Journal Article
%A Segethová, Jitka
%T Elimination on sparse symmetric systems of a special structure
%J Applications of Mathematics
%D 1972
%P 448-460
%V 17
%N 6
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1972.103436/
%R 10.21136/AM.1972.103436
%G en
%F 10_21136_AM_1972_103436
Segethová, Jitka. Elimination on sparse symmetric systems of a special structure. Applications of Mathematics, Tome 17 (1972) no. 6, pp. 448-460. doi: 10.21136/AM.1972.103436

[1] G. G. Alway D. W. Martin: An algorithm for reducing the bandwidth of the matrix of symmetric configuration. Computer J. 8 (1965-66), 264-272.

[2] I. Babuška: Finite element method for domains with corners. Computing 5 (1970), 264-273, | DOI | MR

[3] I. Babuška: The rate of convergence for the finite element method. SIAM J. Numer. Anal. 8 (1971), 304-315. | DOI | MR

[4] E. Cuthill J. McKee: Reducing the bandwidth of sparse symmetric matrices. 1969 Summer National ACM Meeting Proceedings.

[5] F. G. Gustavson W. M. Liniger R. A. Willoughby: Symbolic generation of an optimal Crout algorithm for sparse systems of linear equations. Proc. of the Symposium on Sparse Matr. and Their Appl., IBM Watson Res. Center, 1968.

[6] B. M. Irons: A frontal solution program for finite element analysis. Internat. J. for Num. Meth. in Engineering 2 (1970), 5-32. | DOI | Zbl

[7] S. Parter: The use of linear graphs in Gauss elimination. SIAM Rev. 3 (1961), 119-130. | DOI | MR | Zbl

[8] D. J. Rose: Symmetric elimination on sparse positive definite systems and the potential flow network problem. PhD thesis, Harvard University, Cambridge, Mass., 1970.

[9] R. Rosen: Matrix bandwidth minimization. ACM National Conference Proc., Las Vegas, Nevada, 1968.

[10] J. Segethová: Elimination for sparse symmetric systems of a special structure. Tech. Rep. 70-121, Соmр. Sci. Center, University of Maryland, 1970.

[11] W. R. Spillers N. Hickerson: Optimal elimination for sparse symmetric systems as a graph problem. Quart. Appl. Math. 26 (1968), 425-432. | DOI | MR

[12] R. P. Tewarson: The Gaussian elimination and sparse systems. Proc. of the Symposium on Sparse Matr. and Their Appl., IBM Watson Res. Center, 1968.

Cité par Sources :