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The stability of LU-decompositions of block tridiagonal matrices

Published online by Cambridge University Press:  17 April 2009

R. M. M. Mattheij
R. M. M. Mattheij
Affiliation:
Mathematisch Instituut, Katholieke Universiteit, Nijmegen, The Netherlands; Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12181, USA.
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An investigation is made of the stability of block LU-decomposition of matrices A arising from boundary value problems of differential equations, in particular of ordinary differential equations with separated boundary conditions. It is shown that for such matrices the pivotal growth can be bounded by constants of the order of ‖A‖ and, if solution space is dichotomic, often by constants of order one. Furthermore a method to estimate the growth of the pivotal blocks is given. A number of examples support the analysis.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 29 , Issue 2 , April 1984 , pp. 177 - 205
Copyright
Copyright © Australian Mathematical Society 1984

References

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