Geodesic
Reducing the bandwidth in solving linear algebraic systems arising in the finite element method
Applications of Mathematics, Tome 25 (1980) no. 4, pp. 286-304
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The matrix of the system of linear algebraic equations, arising in the application of the finite element method to one-dimensional problems, is a bandmatrix. In approximations of high order, the band is very wide but the elements situated far from the diagonal of the matrix are negligibly small as compared with the diagonal elements. The aim of the paper is to show on a model problem that in practice it is possible to work with a matrix of the system the bandwidth of which is reduced. A simple numerical example illustates the discussion.
The matrix of the system of linear algebraic equations, arising in the application of the finite element method to one-dimensional problems, is a bandmatrix. In approximations of high order, the band is very wide but the elements situated far from the diagonal of the matrix are negligibly small as compared with the diagonal elements. The aim of the paper is to show on a model problem that in practice it is possible to work with a matrix of the system the bandwidth of which is reduced. A simple numerical example illustates the discussion.
DOI : 10.21136/AM.1980.103862
Classification : 65F30, 65N20
Keywords: reducing the bandwidth; finite element method; numerical example 
@article{10_21136_AM_1980_103862,
     author = {Segethov\'a, Jitka},
     title = {Reducing the bandwidth in solving linear algebraic systems arising in the finite element method},
     journal = {Applications of Mathematics},
     pages = {286--304},
     year = {1980},
     volume = {25},
     number = {4},
     doi = {10.21136/AM.1980.103862},
     mrnumber = {0583589},
     zbl = {0478.65025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1980.103862/}
}
TY  - JOUR
AU  - Segethová, Jitka
TI  - Reducing the bandwidth in solving linear algebraic systems arising in the finite element method
JO  - Applications of Mathematics
PY  - 1980
SP  - 286
EP  - 304
VL  - 25
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1980.103862/
DO  - 10.21136/AM.1980.103862
LA  - en
ID  - 10_21136_AM_1980_103862
ER  - 
%0 Journal Article
%A Segethová, Jitka
%T Reducing the bandwidth in solving linear algebraic systems arising in the finite element method
%J Applications of Mathematics
%D 1980
%P 286-304
%V 25
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1980.103862/
%R 10.21136/AM.1980.103862
%G en
%F 10_21136_AM_1980_103862
Segethová, Jitka. Reducing the bandwidth in solving linear algebraic systems arising in the finite element method. Applications of Mathematics, Tome 25 (1980) no. 4, pp. 286-304. doi: 10.21136/AM.1980.103862

[1] I. Babuška: Approximation by hill functions. Comment. Math. Univ. Carolinae 11 (1970), 787-811. | MR

[2] W. Feller: An introduction to probability theory and its applications. Vol. 2. Wiley, New York 1966. | MR | Zbl

[3] I. S. Gradštein I. M. Ryžik: Tables of integrals, sums, series, and products. (Russian). 5th edition. Nauka, Moskva 1971.

[4] K. Segeth: Universal approximation by hill functions. Czechoslovak Math. J. 22 (1972), 612-640. | MR | Zbl

[5] J. Segethová: Numerical construction of the hill functions. SIAM J. Numer. Anal. 9 (1972), 199-204. | DOI | MR

[6] J. H. Wilkinson: Error analysis of direct methods of matrix inversion. J. Assoc. Comput. Mach. 8 (1961), 281-330. | DOI | MR | Zbl

[7] J. H. Wilkinson: Rounding errors in algebraic processes. HMSO, London 1963. | MR | Zbl

Cité par Sources :