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reducing the bandwidth; finite element method; numerical example
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.
[1] I. Babuška: Approximation by hill functions. Comment. Math. Univ. Carolinae 11 (1970), 787-811. MR 0292309
[2] W. Feller: An introduction to probability theory and its applications. Vol. 2. Wiley, New York 1966. MR 0210154 | Zbl 0138.10207
[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 0310502 | Zbl 0247.41011
[5] J. Segethová: Numerical construction of the hill functions. SIAM J. Numer. Anal. 9 (1972), 199-204. DOI 10.1137/0709018 | MR 0305552
[6] J. H. Wilkinson: Error analysis of direct methods of matrix inversion. J. Assoc. Comput. Mach. 8 (1961), 281-330. DOI 10.1145/321075.321076 | MR 0176602 | Zbl 0109.09005
[7] J. H. Wilkinson: Rounding errors in algebraic processes. HMSO, London 1963. MR 0161456 | Zbl 1041.65502
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