Previous |  Up |  Next


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.
[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 10.1007/BF02238811 | MR 0293858
[3] I. Babuška: The rate of convergence for the finite element method. SIAM J. Numer. Anal. 8 (1971), 304-315. DOI 10.1137/0708031 | MR 0287715
[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 10.1002/nme.1620020104 | Zbl 0252.73050
[7] S. Parter: The use of linear graphs in Gauss elimination. SIAM Rev. 3 (1961), 119-130. DOI 10.1137/1003021 | MR 0143349 | Zbl 0102.11302
[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 10.1090/qam/233497 | MR 0233497
[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.
Partner of
EuDML logo